diff --git a/tests/CMakeLists.txt b/tests/CMakeLists.txt
index c7e2a73d8..1ae06aee9 100644
--- a/tests/CMakeLists.txt
+++ b/tests/CMakeLists.txt
@@ -337,7 +337,6 @@ endif()
 
 find_package(GTest CONFIG)
 find_package(glslang CONFIG)
-find_package(SPIRV-Tools CONFIG)
 
 # Slang
 # ---
@@ -533,7 +532,6 @@ target_link_libraries(vk_layer_validation_tests PRIVATE
     VkLayer_utils
     $<$<BOOL:${USE_SLANG}>:slang>
     glslang::SPIRV
-    SPIRV-Tools-static
     SPIRV-Headers::SPIRV-Headers
     GTest::gtest
     GTest::gtest_main
@@ -542,6 +540,21 @@ target_link_libraries(vk_layer_validation_tests PRIVATE
     $<TARGET_NAME_IF_EXISTS:PkgConfig::WAYlAND_CLIENT>
 )
 
+find_package(SPIRV-Tools CONFIG QUIET)
+
+# See https://github.com/KhronosGroup/SPIRV-Tools/issues/3909 for background on this.
+# The targets available from SPIRV-Tools change depending on how SPIRV_TOOLS_BUILD_STATIC is set.
+# Try to handle all possible combinations so that we work with externally built packages.
+if (TARGET SPIRV-Tools)
+    target_link_libraries(vk_layer_validation_tests PRIVATE SPIRV-Tools)
+elseif(TARGET SPIRV-Tools-static)
+    target_link_libraries(vk_layer_validation_tests PRIVATE SPIRV-Tools-static)
+elseif(TARGET SPIRV-Tools-shared)
+    target_link_libraries(vk_layer_validation_tests PRIVATE SPIRV-Tools-shared)
+else()
+    message(FATAL_ERROR "Cannot determine SPIRV-Tools target name")
+endif(
+
 # setup framework/config.h using framework/config.h.in as a source
 file(GENERATE OUTPUT "${CMAKE_CURRENT_BINARY_DIR}/config_$<CONFIG>.h" INPUT "${CMAKE_CURRENT_SOURCE_DIR}/framework/config.h.in")