diff --git a/copier/main.py b/copier/main.py
index bb514fba0..10255477f 100644
--- a/copier/main.py
+++ b/copier/main.py
@@ -6,9 +6,10 @@
 import subprocess
 import sys
 from contextlib import suppress
+from contextvars import ContextVar
 from dataclasses import asdict, field, replace
 from filecmp import dircmp
-from functools import cached_property, partial
+from functools import cached_property, partial, wraps
 from itertools import chain
 from pathlib import Path
 from shutil import rmtree
@@ -60,6 +61,8 @@
     MISSING,
     AnyByStrDict,
     JSONSerializable,
+    Operation,
+    ParamSpec,
     RelativePath,
     StrOrPath,
 )
@@ -67,6 +70,29 @@
 from .vcs import get_git
 
 _T = TypeVar("_T")
+_P = ParamSpec("_P")
+
+_operation: ContextVar[Operation] = ContextVar("_operation")
+
+
+def as_operation(value: Operation) -> Callable[[Callable[_P, _T]], Callable[_P, _T]]:
+    """Decorator to set the current operation context, if not defined already.
+
+    This value is used to template specific configuration options.
+    """
+
+    def _decorator(func: Callable[_P, _T]) -> Callable[_P, _T]:
+        @wraps(func)
+        def _wrapper(*args: _P.args, **kwargs: _P.kwargs) -> _T:
+            token = _operation.set(_operation.get(value))
+            try:
+                return func(*args, **kwargs)
+            finally:
+                _operation.reset(token)
+
+        return _wrapper
+
+    return _decorator
 
 
 @dataclass(config=ConfigDict(extra="forbid"))
@@ -243,7 +269,7 @@ def _cleanup(self) -> None:
         for method in self._cleanup_hooks:
             method()
 
-    def _check_unsafe(self, mode: Literal["copy", "update"]) -> None:
+    def _check_unsafe(self, mode: Operation) -> None:
         """Check whether a template uses unsafe features."""
         if self.unsafe:
             return
@@ -296,8 +322,10 @@ def _execute_tasks(self, tasks: Sequence[Task]) -> None:
         Arguments:
             tasks: The list of tasks to run.
         """
+        operation = _operation.get()
         for i, task in enumerate(tasks):
             extra_context = {f"_{k}": v for k, v in task.extra_vars.items()}
+            extra_context["_operation"] = operation
 
             if not cast_to_bool(self._render_value(task.condition, extra_context)):
                 continue
@@ -327,7 +355,7 @@ def _execute_tasks(self, tasks: Sequence[Task]) -> None:
                 / Path(self._render_string(str(task.working_directory), extra_context))
             ).absolute()
 
-            extra_env = {k.upper(): str(v) for k, v in task.extra_vars.items()}
+            extra_env = {k[1:].upper(): str(v) for k, v in extra_context.items()}
             with local.cwd(working_directory), local.env(**extra_env):
                 subprocess.run(task_cmd, shell=use_shell, check=True, env=local.env)
 
@@ -588,7 +616,14 @@ def _pathjoin(
     @cached_property
     def match_exclude(self) -> Callable[[Path], bool]:
         """Get a callable to match paths against all exclusions."""
-        return self._path_matcher(self.all_exclusions)
+        # Include the current operation in the rendering context.
+        # Note: This method is a cached property, it needs to be regenerated
+        # when reusing an instance in different contexts.
+        extra_context = {"_operation": _operation.get()}
+        return self._path_matcher(
+            self._render_string(exclusion, extra_context=extra_context)
+            for exclusion in self.all_exclusions
+        )
 
     @cached_property
     def match_skip(self) -> Callable[[Path], bool]:
@@ -818,6 +853,7 @@ def template_copy_root(self) -> Path:
         return self.template.local_abspath / subdir
 
     # Main operations
+    @as_operation("copy")
     def run_copy(self) -> None:
         """Generate a subproject from zero, ignoring what was in the folder.
 
@@ -828,6 +864,11 @@ def run_copy(self) -> None:
 
         See [generating a project][generating-a-project].
         """
+        with suppress(AttributeError):
+            # We might have switched operation context, ensure the cached property
+            # is regenerated to re-render templates.
+            del self.match_exclude
+
         self._check_unsafe("copy")
         self._print_message(self.template.message_before_copy)
         self._ask()
@@ -854,6 +895,7 @@ def run_copy(self) -> None:
             # TODO Unify printing tools
             print("")  # padding space
 
+    @as_operation("copy")
     def run_recopy(self) -> None:
         """Update a subproject, keeping answers but discarding evolution."""
         if self.subproject.template is None:
@@ -864,6 +906,7 @@ def run_recopy(self) -> None:
         with replace(self, src_path=self.subproject.template.url) as new_worker:
             new_worker.run_copy()
 
+    @as_operation("update")
     def run_update(self) -> None:
         """Update a subproject that was already generated.
 
@@ -911,6 +954,11 @@ def run_update(self) -> None:
             print(
                 f"Updating to template version {self.template.version}", file=sys.stderr
             )
+        with suppress(AttributeError):
+            # We might have switched operation context, ensure the cached property
+            # is regenerated to re-render templates.
+            del self.match_exclude
+
         self._apply_update()
         self._print_message(self.template.message_after_update)
 
diff --git a/copier/types.py b/copier/types.py
index be9a5de91..57cf2a067 100644
--- a/copier/types.py
+++ b/copier/types.py
@@ -1,5 +1,6 @@
 """Complex types, annotations, validators."""
 
+import sys
 from pathlib import Path
 from typing import (
     Annotated,
@@ -16,6 +17,11 @@
 
 from pydantic import AfterValidator
 
+if sys.version_info >= (3, 10):
+    from typing import ParamSpec as ParamSpec
+else:
+    from typing_extensions import ParamSpec as ParamSpec
+
 # simple types
 StrOrPath = Union[str, Path]
 AnyByStrDict = Dict[str, Any]
@@ -35,6 +41,7 @@
 Env = Mapping[str, str]
 MissingType = NewType("MissingType", object)
 MISSING = MissingType(object())
+Operation = Literal["copy", "update"]
 
 
 # Validators
diff --git a/docs/configuring.md b/docs/configuring.md
index 636f04ea3..9f5a4d375 100644
--- a/docs/configuring.md
+++ b/docs/configuring.md
@@ -893,6 +893,18 @@ to know available options.
 
 The CLI option can be passed several times to add several patterns.
 
+Each pattern can be templated using Jinja.
+
+!!! example
+
+    Templating `exclude` patterns using `_operation` allows to have files
+    that are rendered once during `copy`, but are never updated:
+
+    ```yaml
+    _exclude:
+        - "{% if _operation == 'update' -%}src/*_example.py{% endif %}"
+    ```
+
 !!! info
 
     When you define this parameter in `copier.yml`, it will **replace** the default
@@ -1351,6 +1363,8 @@ configuring `secret: true` in the [advanced prompt format][advanced-prompt-forma
 exist, but always be present. If they do not exist in a project during an `update`
 operation, they will be recreated.
 
+Each pattern can be templated using Jinja.
+
 !!! example
 
     For example, it can be used if your project generates a password the 1st time and
@@ -1501,6 +1515,9 @@ other items not present.
         - [invoke, end-process, "--full-conf={{ _copier_conf|to_json }}"]
         # Your script can be run by the same Python environment used to run Copier
         - ["{{ _copier_python }}", task.py]
+        # Run a command during the initial copy operation only, excluding updates
+        - command: ["{{ _copier_python }}", task.py]
+          when: "{{ _operation == 'copy' }}"
         # OS-specific task (supported values are "linux", "macos", "windows" and `None`)
         - command: rm {{ name_of_the_project }}/README.md
           when: "{{ _copier_conf.os in  ['linux', 'macos'] }}"
diff --git a/docs/creating.md b/docs/creating.md
index d0415f377..bc43dd828 100644
--- a/docs/creating.md
+++ b/docs/creating.md
@@ -125,6 +125,16 @@ The absolute path of the Python interpreter running Copier.
 
 The name of the project root directory.
 
+## Variables (context-dependent)
+
+Some variables are only available in select contexts:
+
+### `_operation`
+
+The current operation, either `"copy"` or `"update"`.
+
+Availability: [`exclude`](configuring.md#exclude), [`tasks`](configuring.md#tasks)
+
 ## Variables (context-specific)
 
 Some rendering contexts provide variables unique to them:
diff --git a/tests/test_context.py b/tests/test_context.py
new file mode 100644
index 000000000..5479c7db1
--- /dev/null
+++ b/tests/test_context.py
@@ -0,0 +1,90 @@
+import json
+from pathlib import Path
+
+import pytest
+from plumbum import local
+
+import copier
+
+from .helpers import build_file_tree, git_save
+
+
+def test_exclude_templating_with_operation(
+    tmp_path_factory: pytest.TempPathFactory,
+) -> None:
+    """
+    Ensure it's possible to create one-off boilerplate files that are not
+    managed during updates via `_exclude` using the `_operation` context variable.
+    """
+    src, dst = map(tmp_path_factory.mktemp, ("src", "dst"))
+
+    template = "{% if _operation == 'update' %}copy-only{% endif %}"
+    with local.cwd(src):
+        build_file_tree(
+            {
+                "copier.yml": f'_exclude:\n - "{template}"',
+                "{{ _copier_conf.answers_file }}.jinja": "{{ _copier_answers|to_yaml }}",
+                "copy-only": "foo",
+                "copy-and-update": "foo",
+            }
+        )
+        git_save(tag="1.0.0")
+        build_file_tree(
+            {
+                "copy-only": "bar",
+                "copy-and-update": "bar",
+            }
+        )
+        git_save(tag="2.0.0")
+    copy_only = dst / "copy-only"
+    copy_and_update = dst / "copy-and-update"
+
+    copier.run_copy(str(src), dst, defaults=True, overwrite=True, vcs_ref="1.0.0")
+    for file in (copy_only, copy_and_update):
+        assert file.exists()
+        assert file.read_text() == "foo"
+
+    with local.cwd(dst):
+        git_save()
+
+    copier.run_update(str(dst), overwrite=True)
+    assert copy_only.read_text() == "foo"
+    assert copy_and_update.read_text() == "bar"
+
+
+def test_task_templating_with_operation(
+    tmp_path_factory: pytest.TempPathFactory, tmp_path: Path
+) -> None:
+    """
+    Ensure that it is possible to define tasks that are only executed when copying.
+    """
+    src, dst = map(tmp_path_factory.mktemp, ("src", "dst"))
+    # Use a file outside the Copier working directories to ensure accurate tracking
+    task_counter = tmp_path / "task_calls.txt"
+    with local.cwd(src):
+        build_file_tree(
+            {
+                "copier.yml": (
+                    f"""\
+                    _tasks:
+                        -   command: echo {{{{ _operation }}}} >> {json.dumps(str(task_counter))}
+                            when: "{{{{ _operation == 'copy' }}}}"
+                    """
+                ),
+                "{{ _copier_conf.answers_file }}.jinja": "{{ _copier_answers|to_yaml }}",
+            }
+        )
+        git_save(tag="1.0.0")
+
+    copier.run_copy(str(src), dst, defaults=True, overwrite=True, unsafe=True)
+    assert task_counter.exists()
+    assert len(task_counter.read_text().splitlines()) == 1
+
+    with local.cwd(dst):
+        git_save()
+
+    copier.run_recopy(dst, defaults=True, overwrite=True, unsafe=True)
+    assert len(task_counter.read_text().splitlines()) == 2
+
+    copier.run_update(dst, defaults=True, overwrite=True, unsafe=True)
+    assert len(task_counter.read_text().splitlines()) == 2