diff --git a/README.md b/README.md
index 7e4acd4..899497c 100644
--- a/README.md
+++ b/README.md
@@ -19,7 +19,7 @@ pip install flash-attn --no-build-isolation
 
 ## Usage
 
-This repository provides a set of "presses" that compress the KV cache by pruning the least important key-value pairs in each attention head. A press is only applied during the pre-filling phase and is associated with a `compression_ratio` parameter that controls the amount of pruning. The easiest way to use a press is through our custom `KVPressTextGenerationPipeline` that is automatically registered as a transformers pipeline with the name "kv-press-text-generation" when kvpress is imported. It handles chat templates and tokenization for you:
+This repository provides a set of "presses" that compress the KV cache. A press is only applied during the pre-filling phase and is associated with a `compression_ratio` parameter that measures the compression of the cache. The easiest way to use a press is through our custom `KVPressTextGenerationPipeline` that is automatically registered as a transformers pipeline with the name "kv-press-text-generation" when kvpress is imported. It handles chat templates and tokenization for you:
 
 
 
@@ -41,7 +41,7 @@ answer = pipe(context, question=question, press=press)["answer"]
 In the snippet above, the compression is only applied on the context tokens so that you can evaluate the compression for different questions. Check the [Wikipedia notebook demo](notebooks/wikipedia_demo.ipynb) for a more detailed example.
 
 > [!IMPORTANT]  
-> We focus on pruning during the pre-filling phase as the KV cache becomes a bottleneck for long-context sequence (100k - 1M tokens) which are essentially long context prompts. This would typically apply to improving prompt caching systems.
+> We focus on compression during the pre-filling phase as the KV cache becomes a bottleneck for long-context sequence (100k - 1M tokens) which are essentially long context prompts. This would typically apply to improving prompt caching systems.
 
 > [!NOTE]  
 > To use the `ObservedAttentionPress`, use `model_kwargs={"attn_implementation":"eager"}` in order to materialize the attention weights (this method is not compatible with flash attention).
@@ -51,16 +51,23 @@ In the snippet above, the compression is only applied on the context tokens so t
 We welcome contributions! If you want to implement a new press, open an issue or a pull request. Refer to the [FAQ](#faq) for more information on how presses work and how to create new ones or check the [new_press.ipynb](notebooks/new_press.ipynb) notebook for a step-by-step guide.
 
 ## Available presses
-All current presses are training free. We provide the following presses associated with the following scores:
+
+All current presses are training free. Several of them inherit from `ScorerPress` and rely on a score used to prune the KV pairs with lowest importance:
 
 - `RandomPress`: random score
 - `KnormPress`: inverse norm of the key ([paper](https://arxiv.org/abs/2406.11430))
-- `ObservedAttentionPress`: average attention weight observed during in pre-filling phase (similar to [H2O](https://arxiv.org/abs/2306.14048))
 - `SnapKVPress`: average attention weight of the last 64 queries ([paper](https://arxiv.org/abs/2404.14469))
 - `ExpectedAttentionPress` (ours): expected attention weight during the generation phase  (see [this notebook](notebooks/expected_attention.ipynb))
 - `StreamingLLMPress`: keep only the first and last tokens ([paper](https://arxiv.org/abs/2309.17453))
 - `TOVAPress`: attention weight of the last query averaged across heads ([paper](https://arxiv.org/abs/2401.06104))
-- `ThinKPress`: compress the dimension of the keys based on the channel attention score on the last 64 queries ([paper](https://arxiv.org/pdf/2407.21018)). Can be combined with any of the presses above.
+- `ObservedAttentionPress`: average attention weight observed during in pre-filling phase (similar to [H2O](https://arxiv.org/abs/2306.14048))
+
+We also provide presses relying on a different logic:
+- `ThinKPress`: compress the dimension of the keys based on the channel attention score on the last 64 queries ([paper](https://arxiv.org/pdf/2407.21018))
+
+Finally we provide two special presses:
+- `PerLayerCompressionPress`: compress each layer with a different compression ratio (experimental)
+- `ComposedPress`: a press that composes multiple presses together by chaining their forward hooks
 
 For a detailed list of existing KV cache compression methods, check [Awesome-KV-Cache-Compression](https://github.com/October2001/Awesome-KV-Cache-Compression) or [Awesome-LLM-Compression](https://github.com/HuangOwen/Awesome-LLM-Compression?tab=readme-ov-file#kv-cache-compression)
 
diff --git a/kvpress/__init__.py b/kvpress/__init__.py
index 3f80450..fe37d31 100644
--- a/kvpress/__init__.py
+++ b/kvpress/__init__.py
@@ -13,9 +13,11 @@
 from kvpress.presses.snapkv_press import SnapKVPress
 from kvpress.presses.streaming_llm_press import StreamingLLMPress
 from kvpress.presses.think_press import ThinKPress
+from kvpress.presses.composed_press import ComposedPress
 
 __all__ = [
     "BasePress",
+    "ComposedPress",
     "ScorerPress",
     "ExpectedAttentionPress",
     "KnormPress",
diff --git a/kvpress/presses/base_press.py b/kvpress/presses/base_press.py
index 6d30ff4..129d176 100644
--- a/kvpress/presses/base_press.py
+++ b/kvpress/presses/base_press.py
@@ -9,7 +9,14 @@
 
 import torch
 from torch import nn
-from transformers import LlamaForCausalLM, MistralForCausalLM, Phi3ForCausalLM, PreTrainedModel, Qwen2ForCausalLM
+from transformers import (
+    LlamaForCausalLM,
+    MistralForCausalLM,
+    Phi3ForCausalLM,
+    PreTrainedModel,
+    Qwen2ForCausalLM,
+    QuantizedCache,
+)
 
 logger = logging.getLogger(__name__)
 
@@ -17,14 +24,51 @@
 @dataclass
 class BasePress:
     """
-    Base class for all pruning methods.
-    The `forward_hook` method is called after the forward pass of an attention layer.
-    Any pruning/updating method should be implemented in the derived class.
+    Base class for all KV cache compression methods.
+    The `forward_hook` method is called after the forward pass of an attention layer to update the cache.
     """
 
+    def compress(
+        self,
+        module: nn.Module,
+        hidden_states: torch.Tensor,
+        keys: torch.Tensor,
+        values: torch.Tensor,
+        attentions: torch.Tensor,
+        kwargs: dict,
+    ) -> tuple[torch.Tensor, torch.Tensor]:
+        """
+        The core logic of the compression method.
+
+        Parameters
+        ----------
+        module :
+            Transformer layer, see `hook` method for more details
+        hidden_states :
+            Hidden states of the layer
+        keys :
+            Keys of the cache (unquantized)
+        values :
+            Values of the cache (unquantized)
+        attentions :
+            Attention weights of the layer
+        kwargs :
+            Keyword arguments, as given to the forward pass of the layer
+
+        Returns
+        -------
+        tuple[torch.Tensor, torch.Tensor]
+            Updated keys and values
+        """
+
+        raise NotImplementedError("compress method must be implemented in subclass")
+
     def forward_hook(self, module: nn.Module, input: list[torch.Tensor], kwargs: dict, output: list):
-        """Cache compression hook called after the forward pass of an attention layer.
-        The hook is applied only during the pre-filling phase if there is some pruning ratio.
+        """
+        Default forward hook called after the forward pass of an attention layer.
+        The hook calls the compress method to compress the KV cache while ensuring:
+            - compression is only applied only during the pre-filling phase
+            - KV cache quantization is handled correctly
 
         Parameters
         ----------
@@ -40,8 +84,38 @@ def forward_hook(self, module: nn.Module, input: list[torch.Tensor], kwargs: dic
         Returns
         -------
             Modified output of the forward pass of the layer.
+
         """
-        raise NotImplementedError("forward_hook method must be implemented in the derived class")
+        # See e.g. LlamaDecoderLayer.forward for the output structure
+        if len(output) == 3:
+            _, attentions, cache = output
+        else:
+            attentions, cache = None, output[-1]
+
+        hidden_states = kwargs["hidden_states"]
+        q_len = hidden_states.shape[1]
+
+        # Don't compress after pre-filling
+        if cache.seen_tokens > q_len:
+            return output
+
+        if isinstance(cache, QuantizedCache):
+            keys = cache._dequantize(cache._quantized_key_cache[module.layer_idx])
+            values = cache._dequantize(cache._quantized_value_cache[module.layer_idx])
+        else:
+            keys = cache.key_cache[module.layer_idx]
+            values = cache.value_cache[module.layer_idx]
+
+        keys, values = self.compress(module, hidden_states, keys, values, attentions, kwargs)
+
+        if isinstance(cache, QuantizedCache):
+            cache._quantized_key_cache[module.layer_idx] = cache._quantize(keys, axis=cache.axis_key)
+            cache._quantized_value_cache[module.layer_idx] = cache._quantize(values, axis=cache.axis_value)
+        else:
+            cache.key_cache[module.layer_idx] = keys
+            cache.value_cache[module.layer_idx] = values
+
+        return output
 
     @contextmanager
     def __call__(self, model: PreTrainedModel) -> Generator:
diff --git a/kvpress/presses/composed_press.py b/kvpress/presses/composed_press.py
new file mode 100644
index 0000000..3ebc5c1
--- /dev/null
+++ b/kvpress/presses/composed_press.py
@@ -0,0 +1,21 @@
+from dataclasses import dataclass
+from kvpress.presses.base_press import BasePress
+
+
+@dataclass
+class ComposedPress(BasePress):
+    """
+    Chain multiple presses together to create a composed press
+    """
+
+    presses: list[BasePress]
+
+    def __post_init__(self):
+        self.compression_ratio = None
+
+    def forward_hook(self, module, input, kwargs, output):
+        self.compression_ratio = 1.0
+        for press in self.presses:
+            output = press.forward_hook(module, input, kwargs, output)
+            self.compression_ratio *= press.compression_ratio  # type: ignore
+        return output
diff --git a/kvpress/presses/scorer_press.py b/kvpress/presses/scorer_press.py
index a696cc7..ea97eab 100644
--- a/kvpress/presses/scorer_press.py
+++ b/kvpress/presses/scorer_press.py
@@ -7,7 +7,6 @@
 
 import torch
 from torch import nn
-from transformers import QuantizedCache
 
 from kvpress.presses.base_press import BasePress
 
@@ -18,8 +17,9 @@
 class ScorerPress(BasePress):
     """
     Default press method for using a score method.
-    The `forward_hook` method is called after the forward pass of an attention layer.
-    and updates the cache with the pruned KV pairs.
+    Any ScorerPress subclass must implement the `score` method that computes a tensor of scores for each key-value pair
+    The KV pairs with the lowest scores will be pruned in the `compress` method.
+    The cache is uniformly pruned across all heads and layers using the compression_ratio parameter.
     """
 
     compression_ratio: float = 0.0
@@ -36,87 +36,36 @@ def score(
         attentions: torch.Tensor,
         kwargs,
     ) -> torch.Tensor:
-        """Compute the scores for each KV pair in the layer.
-
-        Parameters
-        ----------
-        module :
-            Transformer layer, see `hook` method for more details.
-        hidden_states :
-            Hidden states of the layer.
-        keys :
-            Keys of the cache. Note keys are after RoPE.
-        values :
-            Values of the cache.
-        attentions :
-            Attention weights of the layer.
-        kwargs :
-            Keyword arguments, as given to the forward pass of the layer.
-
-        Returns
-        -------
-            Scores for each KV pair in the layer, shape keys.shape[:-1].
         """
-        raise NotImplementedError
-
-    def forward_hook(self, module: nn.Module, input: list[torch.Tensor], kwargs: dict, output: list):
-        """
-        Default cache compression hook called after the forward pass of an attention layer.
-        The hook is applied only during the pre-filling phase if there is some pruning ratio.
-        This implementation allows to remove a constant number of KV pairs.
-
-        Parameters
-        ----------
-        module :
-            Transformer attention layer.
-        input :
-            Input to the hook. This is the input to the forward pass of the layer.
-        kwargs :
-            Keyword arguments, as given to the forward pass of the layer.
-        output :
-            Output of the hook. This is the original output of the forward pass of the layer.
-
-        Returns
-        -------
-            Modified output of the forward pass of the layer.
-
+        Compute a tensor of scores with shape (bsz, num_key_value_heads, q_len)
+        The KV pairs with lowest scores will be pruned in the `compress` method.
         """
-        # See e.g. LlamaDecoderLayer.forward for the output structure
-        if len(output) == 3:
-            _, attentions, cache = output
-        else:
-            attentions, cache = None, output[-1]
-
-        hidden_states = kwargs["hidden_states"]
-        q_len = hidden_states.shape[1]
+        raise NotImplementedError
 
-        # Don't compress if the compression ratio is 0 or this is not pre-filling
-        if (self.compression_ratio == 0) or (cache.seen_tokens > q_len):
-            return output
+    def compress(
+        self,
+        module: nn.Module,
+        hidden_states: torch.Tensor,
+        keys: torch.Tensor,
+        values: torch.Tensor,
+        attentions: torch.Tensor,
+        kwargs: dict,
+    ) -> tuple[torch.Tensor, torch.Tensor]:
 
-        if isinstance(cache, QuantizedCache):
-            keys = cache._dequantize(cache._quantized_key_cache[module.layer_idx])
-            values = cache._dequantize(cache._quantized_value_cache[module.layer_idx])
-        else:
-            keys = cache.key_cache[module.layer_idx]
-            values = cache.value_cache[module.layer_idx]
+        if self.compression_ratio == 0:
+            return keys, values
 
-        with torch.no_grad():
-            scores = self.score(module, hidden_states, keys, values, attentions, kwargs)
+        # Compute scores
+        scores = self.score(module, hidden_states, keys, values, attentions, kwargs)
 
-        # Prune KV pairs with the lowest scores
+        # Get indices of KV pairs with the lowest scores
+        q_len = hidden_states.shape[1]
         n_kept = int(q_len * (1 - self.compression_ratio))
         indices = scores.topk(n_kept, dim=-1).indices
         indices = indices.unsqueeze(-1).expand(-1, -1, -1, module.head_dim)
 
-        # Update cache
+        # Prune keys and values
         keys = keys.gather(2, indices).contiguous()
         values = values.gather(2, indices).contiguous()
-        if isinstance(cache, QuantizedCache):
-            cache._quantized_key_cache[module.layer_idx] = cache._quantize(keys, axis=cache.axis_key)
-            cache._quantized_value_cache[module.layer_idx] = cache._quantize(values, axis=cache.axis_value)
-        else:
-            cache.key_cache[module.layer_idx] = keys
-            cache.value_cache[module.layer_idx] = values
-
-        return output
+
+        return keys, values
diff --git a/kvpress/presses/think_press.py b/kvpress/presses/think_press.py
index d803387..2f882e5 100644
--- a/kvpress/presses/think_press.py
+++ b/kvpress/presses/think_press.py
@@ -3,11 +3,9 @@
 
 
 from dataclasses import dataclass
-from typing import Optional
 
 import torch
 from torch import nn
-from transformers.cache_utils import QuantizedCache
 from transformers.models.llama.modeling_llama import rotate_half
 
 from kvpress.presses.base_press import BasePress
@@ -18,7 +16,7 @@ class ThinKPress(BasePress):
     """
     ThinK (https://arxiv.org/pdf/2407.21018) compresses the dimensions of the keys, and not the sequence length.
     Hence it can be combined with any other press that compresses the sequence length, e.g.
-    press = ThinKPress(compression_ratio=0.5, inner_press=SnapKVPress(compression_ratio=0.5))
+    press = ComposedPress([SnapKVPress(0.5), ThinKPress(0.5)])
 
     Here, we zero out the pruned dimensions resulting in no memory gain (the shape of the keys remains the same).
     To achieve memory savings, several options can be considered (see https://github.com/NVIDIA/kvpress/pull/18/),
@@ -28,7 +26,6 @@ class ThinKPress(BasePress):
     """
 
     key_channel_compression_ratio: float = 0.0
-    inner_press: Optional[BasePress] = None
     window_size: int = 32
 
     def compute_window_queries(self, module, hidden_states):
@@ -55,36 +52,26 @@ def compute_window_queries(self, module, hidden_states):
 
         return query_states
 
-    def forward_hook(self, module: nn.Module, input: list[torch.Tensor], kwargs: dict, output: list):
+    def compress(
+        self,
+        module: nn.Module,
+        hidden_states: torch.Tensor,
+        keys: torch.Tensor,
+        values: torch.Tensor,
+        attentions: torch.Tensor,
+        kwargs: dict,
+    ) -> tuple[torch.Tensor, torch.Tensor]:
         """
-        We first apply the inner press, then we prune the key dimensions. If other similar presses are requested,
-        we will create a dedicated DimensionBasePress class to avoid code duplication.
+        If other similar presses are requested, we might create a generic compress method for dimension pruning
+        to avoid code duplication.
         """
 
-        # Apply the forward hook of the inner press
-        if self.inner_press is not None:
-            output = self.inner_press.forward_hook(module, input, kwargs, output)
+        if self.key_channel_compression_ratio == 0:
+            return keys, values
 
-        # Don't compress if the compression ratio is 0 or this is not pre-filling
-        cache = output[-1]
-        hidden_states = kwargs["hidden_states"]
-        q_len = hidden_states.shape[1]
-        assert q_len > self.window_size, "Query length should be greater than the window size"
-
-        if (self.key_channel_compression_ratio == 0) or (cache.seen_tokens > q_len):
-            return output
-
-        # Get keys
-        if isinstance(cache, QuantizedCache):
-            keys = cache._dequantize(cache._quantized_key_cache[module.layer_idx])
-        else:
-            keys = cache.key_cache[module.layer_idx]
+        # Compute scores per dimension
         bsz, num_key_value_heads, q_len, head_dim = keys.shape
-
-        # ThinK specific code
         queries = self.compute_window_queries(module, kwargs["hidden_states"])
-
-        # Compute scores per dimension
         queries_norm = torch.pow(queries, 2).mean(dim=2)  # (bsz, num_heads, head_dim)
         queries_norm = queries_norm.view(bsz, num_key_value_heads, module.num_key_value_groups, module.head_dim).mean(2)
         keys_norm = torch.pow(keys, 2).mean(dim=2)
@@ -96,23 +83,12 @@ def forward_hook(self, module: nn.Module, input: list[torch.Tensor], kwargs: dic
         indices = indices.unsqueeze(2).expand(-1, -1, q_len, -1)
         keys = keys.scatter_(-1, indices, 0)
 
-        # Update cache
-        if isinstance(cache, QuantizedCache):
-            cache._quantized_key_cache[module.layer_idx] = cache._quantize(keys, axis=cache.axis_key)
-        else:
-            cache.key_cache[module.layer_idx] = keys
-
-        return output
+        return keys, values
 
     @property
     def compression_ratio(self):
-        compression_ratio = self.key_channel_compression_ratio / 2
-        if self.inner_press is not None and hasattr(self.inner_press, "compression_ratio"):
-            compression_ratio += self.inner_press.compression_ratio
-        return compression_ratio
+        return self.key_channel_compression_ratio / 2
 
     @compression_ratio.setter
     def compression_ratio(self, value):
-        raise AttributeError(
-            "Cannot set the compression ratio of ThinKPress directly. " "Set key_channel_compression_ratio instead."
-        )
+        raise AttributeError(f"compression ratio cannot be set for {type(self).__name__}")
diff --git a/notebooks/new_press.ipynb b/notebooks/new_press.ipynb
index 9d2b0fe..47bba3c 100644
--- a/notebooks/new_press.ipynb
+++ b/notebooks/new_press.ipynb
@@ -10,10 +10,10 @@
    ]
   },
   {
-   "metadata": {},
    "cell_type": "code",
-   "outputs": [],
    "execution_count": null,
+   "metadata": {},
+   "outputs": [],
    "source": [
     "from dataclasses import dataclass\n",
     "\n",
@@ -25,10 +25,10 @@
    ]
   },
   {
-   "metadata": {},
    "cell_type": "code",
-   "outputs": [],
    "execution_count": null,
+   "metadata": {},
+   "outputs": [],
    "source": [
     "# Load pipeline\n",
     "\n",
@@ -39,10 +39,10 @@
    ]
   },
   {
-   "metadata": {},
    "cell_type": "code",
-   "outputs": [],
    "execution_count": null,
+   "metadata": {},
+   "outputs": [],
    "source": [
     "# Load data\n",
     "\n",
@@ -62,10 +62,7 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "\n",
-    "A press registers a forward hook to each attention layer during the pre-filling phase:\n",
-    "1. Immediately after the forward pass, the hook is called, and it computes a score for each key-value pair using the `press.score` method\n",
-    "2. The key-value pairs with the lowest scores are then removed based on the `compression_ratio` parameter"
+    "A press registers a forward hook to each attention layer during the pre-filling phase.  Immediately after the forward pass, the hook is called, and it compresses the KV cache."
    ]
   },
   {
@@ -127,7 +124,6 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "\n",
     "The easiest way to create a new press is to create a class that inherits from `ScorerPress` and implement a `score` method that computes the score for each key-value pair.\n",
     "\n",
     "The arguments of the `score` method are obtained from the forward hook:\n",
@@ -140,10 +136,10 @@
    ]
   },
   {
-   "metadata": {},
    "cell_type": "code",
-   "outputs": [],
    "execution_count": null,
+   "metadata": {},
+   "outputs": [],
    "source": [
     "class MyKnormPress(ScorerPress):\n",
     "    def score(\n",
@@ -181,47 +177,42 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "### 2.2 Updating the `forward_hook` method "
+    "### 2.2 Updating the `compress` method "
    ]
   },
   {
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "The `forward_hook` method defined in the `BasePress` class roughly works as follows:\n",
-    "\n",
-    "1. Get the scores\n",
-    "2. Update the key-value pairs based on the scores and the `compression_ratio`\n",
+    "The `compress` method defined in the `BasePress` contains the core logic of the compression and returns compressed keys and values. For instance, in the `ScorerPress` the `compress` calls the `score` method (which is specific to `ScorerPress`) and prune the key-value pairs based on the scores.\n",
     "\n",
-    "While we generally do not recommend to modify this method, the following example will show how it works. We will re-implement the `StreamingLLMPress` without using the `compression_ratio` parameter. In `StreamingLLM`, only the first `n_first` and last `n_last` key-value pairs are kept."
+    "The following example will show how it works. We will re-implement the `StreamingLLMPress` in a more compact way."
    ]
   },
   {
-   "metadata": {},
    "cell_type": "code",
-   "outputs": [],
    "execution_count": null,
+   "metadata": {},
+   "outputs": [],
    "source": [
     "@dataclass\n",
     "class MyStreamingLLMPress(BasePress):\n",
     "    n_first: int = 1\n",
     "    n_last: int = 8\n",
     "\n",
-    "    def forward_hook(self, module: nn.Module, input: list[torch.Tensor], kwargs: dict, output: list):\n",
-    "\n",
-    "        # Get the cache (transformers.cache_utils.DynamicCache object)\n",
-    "        cache = output[-1]\n",
-    "        i = module.layer_idx\n",
-    "        keys, values = cache.key_cache[i], cache.value_cache[i]\n",
+    "    def compress(\n",
+    "        self,\n",
+    "        module: nn.Module,\n",
+    "        hidden_states: torch.Tensor,\n",
+    "        keys: torch.Tensor,\n",
+    "        values: torch.Tensor,\n",
+    "        attentions: torch.Tensor,\n",
+    "        kwargs: dict,\n",
+    "    ) -> tuple[torch.Tensor, torch.Tensor]:\n",
     "\n",
-    "        # Update the cache to only keep the first and last tokens\n",
     "        mask = torch.ones(keys.shape[-2], dtype=torch.bool, device=keys.device)\n",
     "        mask[self.n_first : -self.n_last] = False\n",
-    "        cache.key_cache[i] = keys[:, :, mask, :]\n",
-    "        cache.value_cache[i] = values[:, :, mask, :]\n",
-    "\n",
-    "        # Return the updated output (output[-1] has been modified in-place)\n",
-    "        return output\n",
+    "        return keys[:, :, mask, :], values[:, :, mask, :]\n",
     "\n",
     "\n",
     "for n_last in [2, 4, 8]:\n",
@@ -231,6 +222,13 @@
     "    print(f\"Answer: {pipe(context, question=question, press=press)['answer']}\")"
    ]
   },
+  {
+   "cell_type": "markdown",
+   "metadata": {},
+   "source": [
+    "Note that in the `compress` method is itself used in the `forward_hook` method which ensures quantization is handled properly and that the compression is only performed during prefilling. While we don't recommend to change the `forward_hook` method directly, you can still modify it if you need to !"
+   ]
+  },
   {
    "cell_type": "markdown",
    "metadata": {},
@@ -242,7 +240,10 @@
    "cell_type": "markdown",
    "metadata": {},
    "source": [
-    "All presses should be stored in the `presses` directory. Before opening a pull request with your new press, make sure to register it in the `__init__.py` file of repository and to add it in [test_presses.py](tests/presses/test_presses.py). We recommend not to update the `forward_hook` or `__call__` method unless necessary."
+    "All presses should be stored in the `presses` directory. Before opening a pull request with your new press, make sure to \n",
+    "- register it in the `__init__.py` file of repository\n",
+    "- add a test [test_presses.py](tests/presses/test_presses.py)\n",
+    "- update the README"
    ]
   }
  ],
@@ -262,7 +263,7 @@
    "name": "python",
    "nbconvert_exporter": "python",
    "pygments_lexer": "ipython3",
-   "version": "3.10.12"
+   "version": "3.12.3"
   }
  },
  "nbformat": 4,
diff --git a/tests/presses/test_presses.py b/tests/presses/test_presses.py
index b1ebae7..07f4008 100644
--- a/tests/presses/test_presses.py
+++ b/tests/presses/test_presses.py
@@ -7,6 +7,7 @@
 from transformers import DynamicCache
 
 from kvpress import (
+    ComposedPress,
     ExpectedAttentionPress,
     KnormPress,
     ObservedAttentionPress,
@@ -20,9 +21,11 @@
 from tests.fixtures import unit_test_model, unit_test_model_output_attention  # noqa: F401
 
 
-def test_think_inner_press(unit_test_model):  # noqa: F811
-    press = ThinKPress(key_channel_compression_ratio=0.5, window_size=2, inner_press=KnormPress(0.5))
-    with press(unit_test_model):
+def test_composed_press(unit_test_model):  # noqa: F811
+    press1 = KnormPress(compression_ratio=0.5)
+    press2 = ThinKPress(key_channel_compression_ratio=0.5, window_size=2)
+    composed_press = ComposedPress([press1, press2])
+    with composed_press(unit_test_model):
         input_ids = unit_test_model.dummy_inputs["input_ids"]
         unit_test_model(input_ids, past_key_values=DynamicCache()).past_key_values
 
@@ -39,6 +42,8 @@ def test_presses_run(unit_test_model):  # noqa: F811
             with press(unit_test_model):
                 input_ids = unit_test_model.dummy_inputs["input_ids"]
                 unit_test_model(input_ids, past_key_values=DynamicCache()).past_key_values
+            # Check that the press has a compression_ratio attribute
+            assert hasattr(press, "compression_ratio")
 
 
 def test_presses_run_observed_attention(unit_test_model_output_attention):  # noqa: F811
diff --git a/tests/test_per_layer_compression_wrapper.py b/tests/test_per_layer_compression_press.py
similarity index 100%
rename from tests/test_per_layer_compression_wrapper.py
rename to tests/test_per_layer_compression_press.py