diff --git a/.github/workflows/ci.yml b/.github/workflows/ci.yml
index 348a982135..9b0b6920c9 100644
--- a/.github/workflows/ci.yml
+++ b/.github/workflows/ci.yml
@@ -23,46 +23,38 @@ jobs:
             os: windows-latest
             bindings_python: ON
             build_shared: OFF
-            unit_tests: ON
             set_path: $env:Path="C:\libxml2\bin;C:\zlib\bin;"+$env:Path
             additional_cmake_options: -DLIBXML2_INCLUDE_DIR="C:\libxml2\include\libxml2" -DLIBXML2_LIBRARY="C:\libxml2\lib\libxml2.lib" -DZLIB_INCLUDE_DIR="C:\zlib\include" -DZLIB_LIBRARY="C:\zlib\lib\z_dll.lib"
           - name: 'Windows shared - C++/Python'
             os: windows-latest
             bindings_python: ON
             build_shared: ON
-            unit_tests: ON
             set_path: $env:Path="C:\libxml2\bin;C:\zlib\bin;"+$env:Path
             additional_cmake_options: -DLIBXML2_INCLUDE_DIR="C:\libxml2\include\libxml2" -DLIBXML2_LIBRARY="C:\libxml2\lib\libxml2.lib" -DZLIB_INCLUDE_DIR="C:\zlib\include" -DZLIB_LIBRARY="C:\zlib\lib\z_dll.lib"
-          - name: 'Linux static - C++ (build only)'
+          - name: 'Linux static - C++'
             os: ubuntu-latest
             bindings_python: OFF
             build_shared: OFF
-            unit_tests: OFF
           - name: 'Linux shared - C++/Python'
             os: ubuntu-latest
             bindings_python: ON
             build_shared: ON
-            unit_tests: ON
           - name: 'macOS static - C++ (Intel)'
             os: macos-13
             bindings_python: OFF
             build_shared: OFF
-            unit_tests: ON
           - name: 'macOS shared - C++/Python (Intel)'
             os: macos-13
             bindings_python: ON
             build_shared: ON
-            unit_tests: ON
           - name: 'macOS static - C++ (ARM)'
             os: macos-latest
             bindings_python: OFF
             build_shared: OFF
-            unit_tests: ON
           - name: 'macOS shared - C++/Python (ARM)'
             os: macos-latest
             bindings_python: ON
             build_shared: ON
-            unit_tests: ON
     steps:
       - name: Check out libCellML
         uses: actions/checkout@v4
@@ -99,13 +91,12 @@ jobs:
           mkdir build
           cd build
           ${{ matrix.set_path }}
-          cmake -G Ninja -DBINDINGS_PYTHON=${{ matrix.bindings_python }} -DBUILD_SHARED=${{ matrix.build_shared }} -DCOVERAGE=OFF -DLLVM_COVERAGE=OFF -DMEMCHECK=OFF -DUNIT_TESTS=${{ matrix.unit_tests }} ${{ matrix.additional_cmake_options }} ..
+          cmake -G Ninja -DBINDINGS_PYTHON=${{ matrix.bindings_python }} -DBUILD_SHARED=${{ matrix.build_shared }} -DCOVERAGE=OFF -DLLVM_COVERAGE=OFF -DMEMCHECK=OFF -DUNIT_TESTS=ON ${{ matrix.additional_cmake_options }} ..
       - name: Build libCellML
         run: |
           cd build
           ninja
       - name: Unit testing
-        if: ${{ matrix.unit_tests == 'ON' }}
         run: |
           cd build
           ninja test
diff --git a/src/CMakeLists.txt b/src/CMakeLists.txt
index b790b2198f..e89a672648 100644
--- a/src/CMakeLists.txt
+++ b/src/CMakeLists.txt
@@ -216,6 +216,10 @@ set_target_properties(cellml PROPERTIES
   COMPATIBLE_INTERFACE_STRING ${PROJECT_VERSION_MAJOR}
 )
 
+if(NOT LIBCELLML_BUILD_SHARED AND CMAKE_SYSTEM_NAME STREQUAL "Linux")
+  set_target_properties(cellml PROPERTIES POSITION_INDEPENDENT_CODE 1)
+endif()
+
 set(DEBUG_SOURCE_FILES
   ${CMAKE_CURRENT_SOURCE_DIR}/debug.cpp
 )
diff --git a/src/bindings/CMakeLists.txt b/src/bindings/CMakeLists.txt
index e981babe02..ded2e1d548 100644
--- a/src/bindings/CMakeLists.txt
+++ b/src/bindings/CMakeLists.txt
@@ -17,6 +17,9 @@ if(LIBCELLML_BINDINGS_PYTHON) # Or any other bindings that use SWIG.
 endif()
 
 if(LIBCELLML_BINDINGS_PYTHON)
+  if(NOT LIBCELLML_BUILD_SHARED)
+    message(WARNING "It is **not** recommended to build the Python bindings with static libraries.")
+  endif()
   add_subdirectory(python)
 endif()
 
diff --git a/src/bindings/python/CMakeLists.txt b/src/bindings/python/CMakeLists.txt
index c98abd754f..966dc02647 100644
--- a/src/bindings/python/CMakeLists.txt
+++ b/src/bindings/python/CMakeLists.txt
@@ -67,7 +67,7 @@ set_source_files_properties(${SWIG_INTERFACE_SRCS} PROPERTIES
 
 set(SETUP_PY_PACKAGE_FILES "'\${TARGET_FILE_NAME_cellml}'")
 list(APPEND FINALISE_PYTHON_BINDINGS_ARGUMENTS -DTARGET_FILE_NAME_cellml=$<TARGET_FILE_NAME:cellml>)
-if (UNIX AND NOT APPLE)
+if (UNIX AND NOT APPLE AND LIBCELLML_BUILD_SHARED)
   list(APPEND SETUP_PY_PACKAGE_FILES "'\${TARGET_SONAME_FILE_NAME_cellml}'")
   list(APPEND FINALISE_PYTHON_BINDINGS_ARGUMENTS -DTARGET_SONAME_FILE_NAME_cellml=$<TARGET_SONAME_FILE_NAME:cellml>)
   set(_GENERATOR_EXPRESSION_LIBCELLML_SONAME $<TARGET_SONAME_FILE:cellml>)
diff --git a/tests/gtest/cmake/internal_utils.cmake b/tests/gtest/cmake/internal_utils.cmake
index 78ab035dff..d73dc4a995 100644
--- a/tests/gtest/cmake/internal_utils.cmake
+++ b/tests/gtest/cmake/internal_utils.cmake
@@ -134,6 +134,7 @@ function(cxx_library_with_type name type cxx_flags)
   add_library(${name} ${type} ${ARGN})
   set_target_properties(${name}
     PROPERTIES
+    POSITION_INDEPENDENT_CODE 1
     COMPILE_FLAGS "${cxx_flags}")
   if (BUILD_SHARED_LIBS OR type STREQUAL "SHARED")
     set_target_properties(${name}