diff --git a/tests/ossfuzz/fuzz_common.h b/tests/ossfuzz/fuzz_common.h
index 4537f1bd..b47a3bdf 100644
--- a/tests/ossfuzz/fuzz_common.h
+++ b/tests/ossfuzz/fuzz_common.h
@@ -20,6 +20,9 @@
 // prevent extreme allocations when fuzzing.
 #define MEM_LIMIT (300 << 20) // 300 MiB
 
+// Amount of input to pass to lzma_code() per call at most.
+#define IN_CHUNK_SIZE 2047
+
 
 static void
 fuzz_code(lzma_stream *stream, const uint8_t *inbuf, size_t inbuf_size) {
@@ -27,15 +30,29 @@ fuzz_code(lzma_stream *stream, const uint8_t *inbuf, size_t inbuf_size) {
 	// cares about the actual data written here.
 	uint8_t outbuf[4096];
 
-	// Give the whole input buffer at once to liblzma.
-	// Output buffer isn't initialized as liblzma only writes to it.
+	// Pass half of the input on the first call and then proceed in
+	// chunks. It's fine that this rounds to 0 when inbuf_size is 1.
 	stream->next_in = inbuf;
-	stream->avail_in = inbuf_size;
-	stream->next_out = outbuf;
-	stream->avail_out = sizeof(outbuf);
+	stream->avail_in = inbuf_size / 2;
+
+	lzma_action action = LZMA_RUN;
 
 	lzma_ret ret;
-	while ((ret = lzma_code(stream, LZMA_FINISH)) == LZMA_OK) {
+	do {
+		if (stream->avail_in == 0 && inbuf_size > 0) {
+			const size_t chunk_size = inbuf_size < IN_CHUNK_SIZE
+					? inbuf_size : IN_CHUNK_SIZE;
+
+			stream->next_in = inbuf;
+			stream->avail_in = chunk_size;
+
+			inbuf += chunk_size;
+			inbuf_size -= chunk_size;
+
+			if (inbuf_size == 0)
+				action = LZMA_FINISH;
+		}
+
 		if (stream->avail_out == 0) {
 			// outbuf became full. We don't care about the
 			// uncompressed data there, so we simply reuse
@@ -43,7 +60,7 @@ fuzz_code(lzma_stream *stream, const uint8_t *inbuf, size_t inbuf_size) {
 			stream->next_out = outbuf;
 			stream->avail_out = sizeof(outbuf);
 		}
-	}
+	} while ((ret = lzma_code(stream, action)) == LZMA_OK);
 
 	// LZMA_PROG_ERROR should never happen as long as the code calling
 	// the liblzma functions is correct. Thus LZMA_PROG_ERROR is a sign