diff --git a/htscodecs/Makefile.am b/htscodecs/Makefile.am
index e4a347d..3dd5e96 100644
--- a/htscodecs/Makefile.am
+++ b/htscodecs/Makefile.am
@@ -104,7 +104,7 @@ libcodecsfuzz_a_SOURCES = $(libhtscodecs_base_src)
 libcodecsfuzz_a_CFLAGS = -fsanitize=fuzzer -DFUZZING_BUILD_MODE_UNSAFE_FOR_PRODUCTION
 libcodecsfuzz_a-htscodecs.$(OBJEXT): version.h
 libcodecsfuzz_sse4_a_SOURCES = rANS_static32x16pr_sse4.c
-libcodecsfuzz_sse4_a_CFLAGS = $(libcodecsfuzz_a_CFLAGS) @MSSE4_1@ @MSSSE3@ @MPOPCNT@
+libcodecsfuzz_sse4_a_CFLAGS = $(libcodecsfuzz_a_CFLAGS) @MSSE4_1@
 libcodecsfuzz_avx2_a_SOURCES = rANS_static32x16pr_avx2.c
 libcodecsfuzz_avx2_a_CFLAGS = $(libcodecsfuzz_a_CFLAGS) @MAVX2@
 libcodecsfuzz_avx512_a_SOURCES = rANS_static32x16pr_avx512.c
diff --git a/tests/fqzcomp_qual_fuzzrt.c b/tests/fqzcomp_qual_fuzzrt.c
index f398841..db75ba0 100644
--- a/tests/fqzcomp_qual_fuzzrt.c
+++ b/tests/fqzcomp_qual_fuzzrt.c
@@ -103,6 +103,10 @@ fqz_slice *fake_slice(size_t buf_len, int nrec) {
 int LLVMFuzzerTestOneInput(uint8_t *in, size_t in_size) {
     size_t c_size, u_size;
 
+    // fake_slice() may need one slice_len[] entry per input byte
+    if (in_size > MAX_REC)
+	return -1;
+
     int mode = 0;
     for (mode = 0; mode < 3; mode++) {
 	int mval[3] = {0,1,in_size};
diff --git a/tests/tokenise_name3_fuzzrt.c b/tests/tokenise_name3_fuzzrt.c
index 878546e..e55c7a8 100644
--- a/tests/tokenise_name3_fuzzrt.c
+++ b/tests/tokenise_name3_fuzzrt.c
@@ -61,7 +61,7 @@ int LLVMFuzzerTestOneInput(const uint8_t *in, size_t in_sz) {
     char in2[8192];
 
     // 4096 is default max size for libfuzzer anyway
-    if (in_sz > 8192)
+    if (in_sz+1 > sizeof(in2)) // +1 for nul below
 	return -1;
 
     // Turn newlines to nuls so we can do round-trip testing