diff --git a/.circleci/config.yml b/.circleci/config.yml
index aa9fa90230..6131d0300d 100644
--- a/.circleci/config.yml
+++ b/.circleci/config.yml
@@ -311,7 +311,7 @@ workflows:
           name: old-cmake
           cc: mpicc -cc=clang
           cxx: mpicxx -cxx=clang++
-          cmake_prefix: /home/builder/local/cmake-3.13.0
+          cmake_prefix: /home/builder/local/cmake-3.16.0
           petsc_dir: /home/builder/local/petsc
           python: "Yes"
 
@@ -331,7 +331,7 @@ workflows:
           name: old-cmake-minimal
           cc: mpicc -cc=clang
           cxx: mpicxx -cxx=clang++
-          cmake_prefix: /home/builder/local/cmake-3.13.0
+          cmake_prefix: /home/builder/local/cmake-3.16.0
 
       - manual-html
       - manual-pdf
diff --git a/CMake/FindUDUNITS2.cmake b/CMake/FindUDUNITS2.cmake
index e0350f3d20..e96e60e12e 100644
--- a/CMake/FindUDUNITS2.cmake
+++ b/CMake/FindUDUNITS2.cmake
@@ -65,23 +65,23 @@ include (CheckCSourceRuns)
 set(CMAKE_REQUIRED_INCLUDES ${UDUNITS2_INCLUDE_DIRS})
 set(CMAKE_REQUIRED_LIBRARIES ${UDUNITS2_LIBRARIES})
 set(CMAKE_REQUIRED_QUIET TRUE)
-check_c_source_runs("${UDUNITS2_TEST_SRC}" UDUNITS2_WORKS_WITHOUT_EXPAT)
+check_c_source_runs("${UDUNITS2_TEST_SRC}" UDUNITS2_WORKS_WITHOUT_LEXPAT)
 
-if(${UDUNITS2_WORKS_WITHOUT_EXPAT})
-  message(STATUS "UDUNITS-2 does not require expat")
+if(${UDUNITS2_WORKS_WITHOUT_LEXPAT})
+  message(STATUS "Linking to UDUNITS-2 does not require '-lexpat'")
 else()
   find_package(EXPAT REQUIRED)
 
   set(CMAKE_REQUIRED_INCLUDES ${UDUNITS2_INCLUDE_DIRS} ${EXPAT_INCLUDE_DIRS})
   set(CMAKE_REQUIRED_LIBRARIES ${UDUNITS2_LIBRARIES} ${EXPAT_LIBRARIES})
   set(CMAKE_REQUIRED_QUIET TRUE)
-  check_c_source_runs("${UDUNITS2_TEST_SRC}" UDUNITS2_WORKS_WITH_EXPAT)
+  check_c_source_runs("${UDUNITS2_TEST_SRC}" UDUNITS2_WORKS_WITH_LEXPAT)
 
-  if(NOT ${UDUNITS2_WORKS_WITH_EXPAT})
-    message(FATAL_ERROR "UDUNITS-2 does not seem to work with or without expat")
+  if(NOT ${UDUNITS2_WORKS_WITH_LEXPAT})
+    message(FATAL_ERROR "UDUNITS-2 does not seem to work with or without -lexpat")
   endif()
 
-  message(STATUS "UDUNITS-2 requires EXPAT")
+  message(STATUS "Using '-lexpat' to link to UDUNITS-2")
   set (UDUNITS2_LIBRARIES "${UDUNITS2_LIBRARIES};${EXPAT_LIBRARIES}" CACHE STRING "" FORCE)
 endif()
 
diff --git a/CMake/PISM_CMake_macros.cmake b/CMake/PISM_CMake_macros.cmake
index 50e883f36a..5c777acce7 100644
--- a/CMake/PISM_CMake_macros.cmake
+++ b/CMake/PISM_CMake_macros.cmake
@@ -133,10 +133,12 @@ function(pism_find_library PREFIX SPEC)
   # Trick pkg-config into using "Libs.private" instead of "Libs" to get the full list of
   # libraries (e.g. not just PETSc, but PETSc and its dependencies). This is needed to
   # build PISM on some systems. See also: https://gitlab.kitware.com/cmake/cmake/-/issues/21714
-  if (CMAKE_VERSION VERSION_LESS "3.22")
-    list(APPEND PKG_CONFIG_EXECUTABLE "--static")
-  else()
-    set(PKG_CONFIG_ARGN "--static" CACHE INTERNAL)
+  if (Pism_PKG_CONFIG_STATIC)
+    if (CMAKE_VERSION VERSION_LESS "3.22")
+      list(APPEND PKG_CONFIG_EXECUTABLE "--static")
+    else()
+      set(PKG_CONFIG_ARGN "--static" CACHE INTERNAL "command-line arguments for pkg-config")
+    endif()
   endif()
   pkg_search_module(${PREFIX} REQUIRED IMPORTED_TARGET ${SPEC})
   if (${${PREFIX}_FOUND})
diff --git a/CMakeLists.txt b/CMakeLists.txt
index e7fe7c896f..69ca9462b3 100644
--- a/CMakeLists.txt
+++ b/CMakeLists.txt
@@ -74,7 +74,8 @@ option (Pism_USE_JANSSON "Use Jansson to read configuration files." OFF)
 option (Pism_TEST_USING_VALGRIND "Add extra regression tests using valgrind" OFF)
 mark_as_advanced (Pism_TEST_USING_VALGRIND)
 
-option (Pism_ADD_FPIC "Add -fPIC to C++ compiler flags (CMAKE_CXX_FLAGS). Try turning it off if it does not work." ON)
+option (Pism_PKG_CONFIG_STATIC "Use the --static pkg-config flag to get linker flags needed by prerequisites" ON)
+option (Pism_ADD_FPIC "Add -fPIC to C & C++ compiler flags. Try turning it off if it does not work." ON)
 option (Pism_CODE_COVERAGE "Add compiler options for code coverage testing." OFF)
 option (Pism_LINK_STATICALLY "Set CMake flags to try to ensure that everything is linked statically")
 option (Pism_LOOK_FOR_LIBRARIES "Specifies whether PISM should look for libraries. (Disable this on Crays.)" ON)
@@ -92,7 +93,7 @@ endif ()
 
 # Add -fPIC to C and CXX flags.
 if (Pism_ADD_FPIC)
-  add_compile_options(-fPIC)
+  set(CMAKE_POSITION_INDEPENDENT_CODE ON)
 endif ()
 
 if (Pism_CODE_COVERAGE)
diff --git a/docker/ubuntu-ci/CMakeLists.txt b/docker/ubuntu-ci/CMakeLists.txt
index fa685b30b5..dbebc49288 100644
--- a/docker/ubuntu-ci/CMakeLists.txt
+++ b/docker/ubuntu-ci/CMakeLists.txt
@@ -4,7 +4,7 @@ foreach(script petsc.sh hdf5.sh netcdf.sh pnetcdf.sh parallelio.sh)
   configure_file(${Pism_SOURCE_DIR}/doc/sphinx/installation/code/${script} . COPYONLY)
 endforeach()
 
-configure_file(cmake-3_13_0.sh . COPYONLY)
+configure_file(cmake-3_16_0.sh . COPYONLY)
 configure_file(old-petsc.sh . COPYONLY)
 
 set(PISM_DOCKER_UBUNTU_VERSION 0.1.8)