diff --git a/src/fuzzers/CMakeLists.txt b/src/fuzzers/CMakeLists.txt
index 97a050d265..74097cb00e 100644
--- a/src/fuzzers/CMakeLists.txt
+++ b/src/fuzzers/CMakeLists.txt
@@ -22,16 +22,26 @@ if ( NOT DEFINED ZEEK_FUZZING_ENGINE AND DEFINED ENV{LIB_FUZZING_ENGINE} )
     endif ()
 endif ()
 
+# The bind library is handled a bit hack-ishly since it defaults to linking it
+# as static library by default on Linux, but at least on one common distro,
+# that static library wasn't compiled with -fPIC and so not usable in the
+# shared library we're trying to build.  So instead, the fuzzer executable, not
+# the shared lib, links it.
+string(REGEX MATCH ".*\\.a$" _have_static_bind_lib "${BIND_LIBRARY}")
+
 macro(ADD_FUZZ_TARGET _name)
     set(_fuzz_target zeek-${_name}-fuzzer)
     set(_fuzz_source ${_name}-fuzzer.cc)
 
     add_executable(${_fuzz_target} ${_fuzz_source} ${ARGN})
 
-    target_link_libraries(${_fuzz_target}
-                          zeek_fuzzer_shared
-                          ${BIND_LIBRARY}
-                          ${CMAKE_THREAD_LIBS_INIT} ${CMAKE_DL_LIBS})
+    target_link_libraries(${_fuzz_target} zeek_fuzzer_shared)
+
+    if ( _have_static_bind_lib )
+        target_link_libraries(${_fuzz_target} ${BIND_LIBRARY})
+    endif ()
+
+    target_link_libraries(${_fuzz_target} ${CMAKE_THREAD_LIBS_INIT} ${CMAKE_DL_LIBS})
 
     if ( DEFINED ZEEK_FUZZING_ENGINE )
         target_link_libraries(${_fuzz_target} ${ZEEK_FUZZING_ENGINE})
@@ -55,12 +65,11 @@ add_library(zeek_fuzzer_shared SHARED
 set(zeek_fuzzer_shared_deps)
 
 foreach(_dep ${zeekdeps} )
-    # The bind library is handled a bit hack-ishly since it defaults to
-    # linking it as static library by default on Linux, but at least
-    # on one common distro, that static library wasn't compiled with -fPIC
-    # and so not usable in the shared library we're trying to build.
-    # So instead, the fuzzer executable, not the shared lib, links it.
-    if ( NOT "${_dep}" STREQUAL "${BIND_LIBRARY}" )
+    if ( "${_dep}" STREQUAL "${BIND_LIBRARY}" )
+        if ( NOT _have_static_bind_lib )
+            set(zeek_fuzzer_shared_deps ${zeek_fuzzer_shared_deps} ${_dep})
+        endif ()
+    else ()
         set(zeek_fuzzer_shared_deps ${zeek_fuzzer_shared_deps} ${_dep})
     endif ()
 endforeach ()