diff --git a/cookiecutter/generate.py b/cookiecutter/generate.py
index 4739aec..4656a4f 100644
--- a/cookiecutter/generate.py
+++ b/cookiecutter/generate.py
@@ -323,6 +323,7 @@ def generate_files(
             for copy_dir in copy_dirs:
                 indir = os.path.normpath(os.path.join(root, copy_dir))
                 outdir = os.path.normpath(os.path.join(project_dir, indir))
+                outdir = env.from_string(outdir).render(**context)
                 logger.debug('Copying dir %s to %s without rendering', indir, outdir)
                 shutil.copytree(indir, outdir)
 
diff --git a/docs/advanced/copy_without_render.rst b/docs/advanced/copy_without_render.rst
index a804032..2cdb680 100644
--- a/docs/advanced/copy_without_render.rst
+++ b/docs/advanced/copy_without_render.rst
@@ -15,3 +15,14 @@ To avoid rendering directories and files of a cookiecutter, the `_copy_without_r
             "rendered_dir/not_rendered_file.ini"
         ]
     }
+
+**Note**: Only the content of the files will be copied without being rendered. The paths are subject to rendering. This allows you to write::
+
+    {
+        "project_slug": "sample",
+        "_copy_without_render": [
+            "{{cookiecutter.repo_name}}/templates/*.html",
+        ]
+    }
+
+In this example, `{{cookiecutter.repo_name}}` will be rendered as expected but the html file content will be copied without rendering.

Allow for copy_without_render to render output directory name
I find it strange that copy_without_render doesn't render the directory name.

An example use case is wanting to copy a templates directory in your project that contains jinja, the directory is copied however it is placed into a folder like '{{cookiecutter.repo_name}}/templates' as opposed to 'someproject/templates'

I understand some people may in fact want this, but maybe an option to to toggle this behavior would welcome. 

diff --git a/tests/test-generate-copy-without-render/{{cookiecutter.repo_name}}/{{cookiecutter.repo_name}}-rendered/README.md b/tests/test-generate-copy-without-render/{{cookiecutter.repo_name}}/{{cookiecutter.repo_name}}-rendered/README.md
new file mode 100644
index 0000000..0e74081
--- /dev/null
+++ b/tests/test-generate-copy-without-render/{{cookiecutter.repo_name}}/{{cookiecutter.repo_name}}-rendered/README.md
@@ -0,0 +1,3 @@
+# Fake Project
+
+{{cookiecutter.render_test}}
diff --git a/tests/test_generate_copy_without_render.py b/tests/test_generate_copy_without_render.py
index 0e2a944..7d61482 100644
--- a/tests/test_generate_copy_without_render.py
+++ b/tests/test_generate_copy_without_render.py
@@ -31,6 +31,7 @@ def test_generate_copy_without_render_extensions():
                     '*not-rendered',
                     'rendered/not_rendered.yml',
                     '*.txt',
+                    '{{cookiecutter.repo_name}}-rendered/README.md',
                 ],
             }
         },
@@ -39,7 +40,7 @@ def test_generate_copy_without_render_extensions():
 
     dir_contents = os.listdir('test_copy_without_render')
 
-    assert '{{cookiecutter.repo_name}}-not-rendered' in dir_contents
+    assert 'test_copy_without_render-not-rendered' in dir_contents
     assert 'test_copy_without_render-rendered' in dir_contents
 
     with open('test_copy_without_render/README.txt') as f:
@@ -59,9 +60,16 @@ def test_generate_copy_without_render_extensions():
         assert 'I have been rendered' in f.read()
 
     with open(
-        'test_copy_without_render/{{cookiecutter.repo_name}}-not-rendered/README.rst'
+        'test_copy_without_render/'
+        'test_copy_without_render-not-rendered/'
+        'README.rst'
     ) as f:
         assert '{{cookiecutter.render_test}}' in f.read()
 
     with open('test_copy_without_render/rendered/not_rendered.yml') as f:
         assert '{{cookiecutter.render_test}}' in f.read()
+
+    with open(
+        'test_copy_without_render/' 'test_copy_without_render-rendered/' 'README.md'
+    ) as f:
+        assert '{{cookiecutter.render_test}}' in f.read()

pip install -e .[dev]
parse_log_pytest
scipy numpy
pytest pytest-cov pytest-mock
3.7
pytest --no-header -rA --tb=line --color=no -p no:cacheprovider -W ignore::DeprecationWarning
arrow==1.2.3
binaryornot==0.4.4
certifi @ file:///croot/certifi_1671487769961/work/certifi
chardet==5.2.0
charset-normalizer==3.4.1
click==8.1.8
-e git+https://github.com/cookiecutter/cookiecutter.git@d8672b11e445a918431933c322e7ac96440fd438#egg=cookiecutter
coverage==7.2.7
exceptiongroup==1.2.2
idna==3.10
importlib-metadata==6.7.0
iniconfig==2.0.0
Jinja2==2.11.3
jinja2-time==0.2.0
MarkupSafe==1.1.1
numpy @ file:///opt/conda/conda-bld/numpy_and_numpy_base_1653915516269/work
packaging==24.0
pluggy==1.2.0
poyo==0.5.0
pytest==7.4.4
pytest-cov==4.1.0
pytest-mock==3.11.1
python-dateutil==2.9.0.post0
python-slugify==8.0.4
requests==2.31.0
scipy @ file:///opt/conda/conda-bld/scipy_1661390393401/work
six==1.17.0
text-unidecode==1.3
tomli==2.0.1
typing_extensions==4.7.1
urllib3==2.0.7
zipp==3.15.0

name: cookiecutter
channels:
  - defaults
  - https://repo.anaconda.com/pkgs/main
  - https://repo.anaconda.com/pkgs/r
  - conda-forge
dependencies:
  - _libgcc_mutex=0.1=main
  - _openmp_mutex=5.1=1_gnu
  - blas=1.0=openblas
  - ca-certificates=2025.2.25=h06a4308_0
  - certifi=2022.12.7=py37h06a4308_0
  - fftw=3.3.9=h5eee18b_2
  - ld_impl_linux-64=2.40=h12ee557_0
  - libffi=3.4.4=h6a678d5_1
  - libgcc-ng=11.2.0=h1234567_1
  - libgfortran-ng=11.2.0=h00389a5_1
  - libgfortran5=11.2.0=h1234567_1
  - libgomp=11.2.0=h1234567_1
  - libopenblas=0.3.21=h043d6bf_0
  - libstdcxx-ng=11.2.0=h1234567_1
  - ncurses=6.4=h6a678d5_0
  - numpy=1.21.5=py37hf838250_3
  - numpy-base=1.21.5=py37h1e6e340_3
  - openssl=1.1.1w=h7f8727e_0
  - pip=22.3.1=py37h06a4308_0
  - python=3.7.16=h7a1cb2a_0
  - readline=8.2=h5eee18b_0
  - scipy=1.7.3=py37hf838250_2
  - setuptools=65.6.3=py37h06a4308_0
  - sqlite=3.45.3=h5eee18b_0
  - tk=8.6.14=h39e8969_0
  - wheel=0.38.4=py37h06a4308_0
  - xz=5.6.4=h5eee18b_1
  - zlib=1.2.13=h5eee18b_1
  - pip:
      - arrow==1.2.3
      - binaryornot==0.4.4
      - chardet==5.2.0
      - charset-normalizer==3.4.1
      - click==8.1.8
      - cookiecutter==2.0.0
      - coverage==7.2.7
      - exceptiongroup==1.2.2
      - idna==3.10
      - importlib-metadata==6.7.0
      - iniconfig==2.0.0
      - jinja2==2.11.3
      - jinja2-time==0.2.0
      - markupsafe==1.1.1
      - packaging==24.0
      - pluggy==1.2.0
      - poyo==0.5.0
      - pytest==7.4.4
      - pytest-cov==4.1.0
      - pytest-mock==3.11.1
      - python-dateutil==2.9.0.post0
      - python-slugify==8.0.4
      - requests==2.31.0
      - six==1.17.0
      - text-unidecode==1.3
      - tomli==2.0.1
      - typing-extensions==4.7.1
      - urllib3==2.0.7
      - zipp==3.15.0
prefix: /opt/conda/envs/cookiecutter

tests/test_generate_copy_without_render.py::test_generate_copy_without_render_extensions
cookiecutter/generate.py docs/advanced/copy_without_render.rst
cookiecutter/generate.py docs/advanced/copy_without_render.rst