diff --git a/CMakeLists.txt b/CMakeLists.txt
index c9f7f87..df08a39 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -14,6 +14,8 @@
 # Add a CMake parameter for choosing a desired Python version
 set(PYBIND11_PYTHON_VERSION "" CACHE STRING "Python version to use for compiling the example application")
 
+include(CheckCXXCompilerFlag)
+
 # Set a default build configuration if none is specified. 'MinSizeRel' produces the smallest binaries
 if(NOT CMAKE_BUILD_TYPE AND NOT CMAKE_CONFIGURATION_TYPES)
   message(STATUS "Setting build type to 'MinSizeRel' as none was specified.")
@@ -23,11 +25,16 @@
 endif()
 string(TOUPPER "${CMAKE_BUILD_TYPE}" U_CMAKE_BUILD_TYPE)
 
-set(Python_ADDITIONAL_VERSIONS 3.4 3.5 3.6)
-find_package(PythonLibs ${PYBIND11_PYTHON_VERSION} REQUIRED)
-find_package(PythonInterp ${PYBIND11_PYTHON_VERSION} REQUIRED)
-
-include(CheckCXXCompilerFlag)
+set(Python_ADDITIONAL_VERSIONS 3.4 3.5 3.6 3.7)
+if (NOT ${PYBIND11_PYTHON_VERSION} STREQUAL "")
+  find_package(PythonLibs ${PYBIND11_PYTHON_VERSION} EXACT)
+  if (NOT PythonLibs_FOUND)
+    find_package(PythonLibs ${PYBIND11_PYTHON_VERSION} REQUIRED)
+  endif()
+else()
+  find_package(PythonLibs REQUIRED)
+endif()
+find_package(PythonInterp ${PYTHONLIBS_VERSION_STRING} EXACT REQUIRED)
 
 if (CMAKE_CXX_COMPILER_ID MATCHES "Clang" OR CMAKE_CXX_COMPILER_ID MATCHES "GNU")
   # Enable C++11 mode on C++ / Clang
diff --git a/docs/cmake.rst b/docs/cmake.rst
index 5952920..348c54a 100644
--- a/docs/cmake.rst
+++ b/docs/cmake.rst
@@ -28,8 +28,15 @@
     string(TOUPPER "${CMAKE_BUILD_TYPE}" U_CMAKE_BUILD_TYPE)
 
     # Try to autodetect Python (can be overridden manually if needed)
-    set(Python_ADDITIONAL_VERSIONS 3.4 3.5 3.6)
-    find_package(PythonLibs ${EXAMPLE_PYTHON_VERSION} REQUIRED)
+    set(Python_ADDITIONAL_VERSIONS 3.4 3.5 3.6 3.7)
+    if (NOT ${PYBIND11_PYTHON_VERSION} STREQUAL "")
+      find_package(PythonLibs ${PYBIND11_PYTHON_VERSION} EXACT REQUIRED)
+    else()
+      find_package(PythonLibs REQUIRED)
+    endif()
+
+    # Uncomment the following line if you will also require a matching Python interpreter
+    # find_package(PythonInterp ${PYTHONLIBS_VERSION_STRING} EXACT REQUIRED)
 
     if (CMAKE_CXX_COMPILER_ID MATCHES "Clang" OR CMAKE_CXX_COMPILER_ID MATCHES "GNU")
       # Enable C++11 mode on C++ / Clang