diff --git a/README.md b/README.md
index 208158d..532187f 100644
--- a/README.md
+++ b/README.md
@@ -102,7 +102,7 @@ To get started:
 
 #### Prerequisites
 
-1. **Python 3.10+**: We recommend using [pyenv](https://github.com/pyenv/pyenv) or
+1. **Python 3.11+**: We recommend using [pyenv](https://github.com/pyenv/pyenv) or
    [uv](https://docs.astral.sh/uv/) for managing Python versions.
 2. **[Pip](https://pip.pypa.io/en/stable/installation/) or [Pipx](https://pipx.pypa.io/stable/)**
 3. **[Copier](https://github.com/copier-org/copier)**: Install Copier using pip or pipx.
diff --git a/copier.yml b/copier.yml
index 942b9ff..ffaf359 100644
--- a/copier.yml
+++ b/copier.yml
@@ -71,7 +71,7 @@ repository_visibility:
     - internal
     - private
 
-repository_slug:
+default_module_name:
   type: str
   help: "Not prompted. This is computed for re-use."
   default: "{{ repository_name | lower | replace('-', '_') | replace(' ', '_') }}"
@@ -85,11 +85,11 @@ is_public_repo:
 
 module_name:
   type: str
-  help: "What is your Python module name? (e.g. app/src/{{ repository_slug }})"
-  default: "{{ repository_slug }}"
+  help: "What is your Python module name? (e.g. app / src / {{ default_module_name }})"
+  default: "{{ default_module_name }}"
   validator: >-
-    {% if not (module_name | regex_search('^[a-z][a-z0-9\_\-]+$')) %}
-    Must use a lowercase letter followed by one or more of (a-z, 0-9, _, -).
+    {% if not (module_name | regex_search('^[a-z][a-z0-9_]*$')) %}
+    Must be a valid Python package name: start with a lowercase letter and use only lowercase letters, numbers, and underscores.
     {% endif %}
 
 enable_dependabot_version_updates:
diff --git a/tests/test_template_generation.py b/tests/test_template_generation.py
index f852333..6af7a88 100644
--- a/tests/test_template_generation.py
+++ b/tests/test_template_generation.py
@@ -2,6 +2,8 @@
 
 from __future__ import annotations
 
+import subprocess
+import sys
 from pathlib import Path
 from typing import Any
 
@@ -28,6 +30,16 @@ def read_pre_commit_config(destination: Path) -> str:
     return (destination / ".pre-commit-config.yaml").read_text(encoding="utf-8")
 
 
+def assert_python_files_compile(*paths: Path) -> None:
+    """Assert that rendered Python files are syntactically valid."""
+    subprocess.run(
+        [sys.executable, "-m", "py_compile", *[str(path) for path in paths]],
+        check=True,
+        capture_output=True,
+        text=True,
+    )
+
+
 def assert_public_visibility_outputs(destination: Path) -> None:
     """Assert the public-repository specific files and README content."""
     assert (destination / "LICENSE").exists()
@@ -244,8 +256,6 @@ def test_uv_generation_requires_confirmation(
     generated_project_dir: Path,
 ) -> None:
     """The uv option should reject an explicit decision not to use uv."""
-    import subprocess
-
     with pytest.raises(subprocess.CalledProcessError) as exc_info:
         copier_runner.copy(
             generated_project_dir,
@@ -255,3 +265,38 @@ def test_uv_generation_requires_confirmation(
         )
 
     assert "You must confirm the use of uv to continue" in exc_info.value.stderr
+
+
+def test_valid_custom_module_name_generates_importable_python(
+    copier_runner: Any,
+    generated_project_dir: Path,
+) -> None:
+    """A custom module name using underscores should render valid Python imports."""
+    copier_runner.copy(
+        generated_project_dir,
+        repository_visibility="public",
+        package_manager="poetry",
+        module_name="custom_module",
+    )
+
+    assert (generated_project_dir / "custom_module").exists()
+    assert_python_files_compile(
+        generated_project_dir / "custom_module" / "__main__.py",
+        generated_project_dir / "tests" / "unit" / "conftest.py",
+    )
+
+
+def test_hyphenated_module_name_is_rejected(
+    copier_runner: Any,
+    generated_project_dir: Path,
+) -> None:
+    """A hyphenated module name should fail validation because it is not import-safe."""
+    with pytest.raises(subprocess.CalledProcessError) as exc_info:
+        copier_runner.copy(
+            generated_project_dir,
+            repository_visibility="public",
+            package_manager="poetry",
+            module_name="bad-name",
+        )
+
+    assert "valid Python package name" in exc_info.value.stderr