diff --git a/src/fuzzers/FuzzBuffer.cc b/src/fuzzers/FuzzBuffer.cc
index ebae1a1db1..098ce92f5c 100644
--- a/src/fuzzers/FuzzBuffer.cc
+++ b/src/fuzzers/FuzzBuffer.cc
@@ -17,6 +17,23 @@ bool zeek::detail::FuzzBuffer::Valid() const
 	return true;
 	}
 
+int zeek::detail::FuzzBuffer::ChunkCount() const
+	{
+	auto pos = begin;
+	int chunks = 0;
+	while (pos < end)
+		{
+		pos = (const unsigned char*)memmem(pos, end - pos,
+		                                   PKT_MAGIC, PKT_MAGIC_LEN);
+		if ( ! pos )
+			break;
+		pos += PKT_MAGIC_LEN + 1;
+		chunks++;
+		}
+
+	return chunks;
+	}
+
 std::optional<zeek::detail::FuzzBuffer::Chunk> zeek::detail::FuzzBuffer::Next()
 	{
 	if ( begin == end )
diff --git a/src/fuzzers/FuzzBuffer.h b/src/fuzzers/FuzzBuffer.h
index 1b9cdb58a3..f79f20091e 100644
--- a/src/fuzzers/FuzzBuffer.h
+++ b/src/fuzzers/FuzzBuffer.h
@@ -43,6 +43,11 @@ public:
 	 */
 	bool Valid() const;
 
+	/**
+	 * @return  the number of chunks in the fuzz buffer object
+	 */
+	int ChunkCount() const;
+
 	/**
 	 * @return  the next chunk to deliver, if one could be extracted
 	 */
diff --git a/src/fuzzers/packet-fuzzer.cc b/src/fuzzers/packet-fuzzer.cc
index d3bb28b806..59002f6c79 100644
--- a/src/fuzzers/packet-fuzzer.cc
+++ b/src/fuzzers/packet-fuzzer.cc
@@ -18,6 +18,9 @@ extern "C" int LLVMFuzzerTestOneInput(const uint8_t* data, size_t size)
 	if ( ! fb.Valid() )
 		return 0;
 
+	if ( fb.ChunkCount() > 64 )
+		return 0;
+
 	for ( ; ;  )
 		{
 		auto chunk = fb.Next();
diff --git a/src/fuzzers/pop3-fuzzer.cc b/src/fuzzers/pop3-fuzzer.cc
index 5cc4776aad..2c6e01fc5c 100644
--- a/src/fuzzers/pop3-fuzzer.cc
+++ b/src/fuzzers/pop3-fuzzer.cc
@@ -50,6 +50,9 @@ extern "C" int LLVMFuzzerTestOneInput(const uint8_t* data, size_t size)
 	if ( ! fb.Valid() )
 		return 0;
 
+	if ( fb.ChunkCount() > 64 )
+		return 0;
+
 	auto conn = add_connection();
 	auto a = add_analyzer(conn);