diff --git a/.appveyor.yml b/.appveyor.yml
index b9b862a..f4d7e89 100644
--- a/.appveyor.yml
+++ b/.appveyor.yml
@@ -21,12 +21,12 @@ before_build:
 - mkdir build
 - mkdir libepoxy-shared-%pout%
 - cd build
-- curl -LsSO https://github.com/mesonbuild/meson/releases/download/0.38.0/meson-0.38.0.tar.gz
-- 7z x meson-0.38.0.tar.gz
-- move dist\meson-0.38.0.tar .
-- 7z x meson-0.38.0.tar
+- curl -LsSO https://github.com/mesonbuild/meson/releases/download/0.39.1/meson-0.39.1.tar.gz
+- 7z x meson-0.39.1.tar.gz
+- move dist\meson-0.39.1.tar .
+- 7z x meson-0.39.1.tar
 - rmdir dist
-- del meson-0.38.0.tar meson-0.38.0.tar.gz
+- del meson-0.39.1.tar meson-0.39.1.tar.gz
 - curl -LsSO https://github.com/ninja-build/ninja/releases/download/v1.7.2/ninja-win.zip
 - 7z x ninja-win.zip
 - del ninja-win.zip
@@ -36,7 +36,7 @@ before_build:
 build_script:
 - cd build
 - call "C:\Program Files (x86)\Microsoft Visual Studio 14.0\VC\vcvarsall.bat" %PLATFORM%
-- C:\Python36\python.exe meson-0.38.0\meson.py .. . --backend=ninja --prefix=%APPVEYOR_BUILD_FOLDER%\libepoxy-shared-%pout%
+- C:\Python36\python.exe meson-0.39.1\meson.py .. . --backend=ninja --prefix=%APPVEYOR_BUILD_FOLDER%\libepoxy-shared-%pout%
 - ninja
 - ninja install
 - cd ..
diff --git a/include/epoxy/meson.build b/include/epoxy/meson.build
index 12ae719..65f83be 100644
--- a/include/epoxy/meson.build
+++ b/include/epoxy/meson.build
@@ -39,4 +39,6 @@ foreach g: generated_headers
   headers += [ header ]
 endforeach
 
+epoxy_headers = files(headers) + gen_headers
+
 install_headers(headers, subdir: 'epoxy')
diff --git a/meson.build b/meson.build
index 7d9afd9..ae0cc88 100644
--- a/meson.build
+++ b/meson.build
@@ -5,7 +5,7 @@ project('libepoxy', 'c', version: '1.4.1',
           'warning_level=1',
         ],
         license: 'MIT',
-        meson_version: '>= 0.36.0')
+        meson_version: '>= 0.38.1')
 
 epoxy_version = meson.project_version().split('.')
 epoxy_major_version = epoxy_version[0].to_int()
@@ -223,17 +223,13 @@ configure_file(input: 'epoxy.pc.in',
                install_dir: join_paths(epoxy_libdir, 'pkgconfig'))
 
 # Python
-# XXX: Depend on 0.37.1 for:
-# python = import('python3').find_python()
-python = find_program('python3', required: false)
+python = import('python3').find_python()
 if not python.found()
   python = find_program('python', required: true)
 endif
 
 # Generates the dispatch tables
-# XXX: Depend on 0.38.1 for:
-# gen_dispatch_py = files('src/gen_dispatch.py')
-gen_dispatch_py = join_paths(meson.source_root(), 'src/gen_dispatch.py')
+gen_dispatch_py = files('src/gen_dispatch.py')
 
 gl_registry = files('registry/gl.xml')
 egl_registry = files('registry/egl.xml')
diff --git a/src/meson.build b/src/meson.build
index ce6fe45..6f44220 100644
--- a/src/meson.build
+++ b/src/meson.build
@@ -46,10 +46,6 @@ foreach g: generated_sources
 endforeach
 
 epoxy_sources = sources + gen_sources
-epoxy_headers = gen_headers
-foreach h: headers
-  epoxy_headers += join_paths(meson.source_root(), 'include/epoxy/@0@'.format(h))
-endforeach
 
 common_ldflags = []