diff --git a/flake8_simplify.py b/flake8_simplify.py
index ecb68b0..f730848 100644
--- a/flake8_simplify.py
+++ b/flake8_simplify.py
@@ -1093,24 +1093,41 @@ def _get_sim119(node: ast.ClassDef) -> List[Tuple[int, int, str]]:
         "__repr__",
         "__str__",
     ]
-    has_only_constructur_function = True
+    has_only_dataclass_functions = True
+    has_any_functions = False
     for body_el in node.body:
-        if (
-            isinstance(body_el, ast.FunctionDef)
-            and body_el.name not in dataclass_functions
-        ):
-            has_only_constructur_function = False
-            break
+        if isinstance(body_el, (ast.FunctionDef, ast.AsyncFunctionDef)):
+            has_any_functions = True
+            if body_el.name == "__init__":
+                # Ensure constructor only has pure assignments
+                # without any calculation.
+                has_complex_statements = False
+                for el in body_el.body:
+                    if not isinstance(el, ast.Assign):
+                        has_complex_statements = True
+                        break
+                    else:
+                        # It is an assignment, but we only allow
+                        # `self.attribute = name`.
+                        if any(
+                            [
+                                not isinstance(target, ast.Attribute)
+                                for target in el.targets
+                            ]
+                        ) or not isinstance(el.value, ast.Name):
+                            has_complex_statements = True
+                            break
+            if body_el.name not in dataclass_functions:
+                has_only_dataclass_functions = False
 
-    if not (
-        has_only_constructur_function
-        and sum(1 for el in node.body if isinstance(el, ast.FunctionDef)) > 0
+    if (
+        has_any_functions
+        and has_only_dataclass_functions
+        and not has_complex_statements
     ):
-        return errors
-
-    errors.append(
-        (node.lineno, node.col_offset, SIM119.format(classname=node.name))
-    )
+        errors.append(
+            (node.lineno, node.col_offset, SIM119.format(classname=node.name))
+        )
 
     return errors
 
diff --git a/tests/test_simplify.py b/tests/test_simplify.py
index 1f791a7..24ba5dd 100644
--- a/tests/test_simplify.py
+++ b/tests/test_simplify.py
@@ -476,6 +476,25 @@ def test_sim118_del_key():
 def test_sim119():
     results = _results(
         """
+class FooBar:
+    def __init__(self, a, b):
+        self.a = a
+        self.b = b
+"""
+    )
+    assert results == {"2:0 SIM119 Use a dataclass for 'class FooBar'"}
+
+
+def test_sim119_ignored_dunder_methods():
+    """
+    Dunder methods do not make a class not be a dataclass candidate.
+    Examples for dunder (double underscore) methods are:
+      * __str__
+      * __eq__
+      * __hash__
+    """
+    results = _results(
+        """
 class FooBar:
     def __init__(self, a, b):
         self.a = a
@@ -488,6 +507,32 @@ def __str__(self):
     assert results == {"2:0 SIM119 Use a dataclass for 'class FooBar'"}
 
 
+def test_sim119_async():
+    results = _results(
+        """
+class FooBar:
+    def __init__(self, a, b):
+        self.a = a
+        self.b = b
+
+    async def foo(self):
+        return "FooBar"
+"""
+    )
+    assert results == set()
+
+
+def test_sim119_constructor_processing():
+    results = _results(
+        """
+class FooBar:
+    def __init__(self, a):
+        self.a = a + 5
+"""
+    )
+    assert results == set()
+
+
 def test_sim119_pydantic():
     results = _results(
         """