diff --git a/tests/fuzz/ssh_client_fuzzer.c b/tests/fuzz/ssh_client_fuzzer.c
index 2e3a0da6..304b038c 100644
--- a/tests/fuzz/ssh_client_fuzzer.c
+++ b/tests/fuzz/ssh_client_fuzzer.c
@@ -94,6 +94,14 @@ int LLVMFuzzerTestOneInput(const uint8_t *data, size_t size)
     bool no = false;
     int rc;
 
+    /* This is the maximum that can be handled by the socket buffer before the
+     * other side will read some data. Other option would be feeding the socket
+     * from different thread which would not mind if it would be blocked, but I
+     * believe all the important inputs should fit into this size */
+    if (size > 219264) {
+        return -1;
+    }
+
     /* Set up the socket to send data */
     rc = socketpair(AF_UNIX, SOCK_STREAM, 0, socket_fds);
     assert(rc == 0);
diff --git a/tests/fuzz/ssh_server_fuzzer.c b/tests/fuzz/ssh_server_fuzzer.c
index 2d830cfc..c20ae373 100644
--- a/tests/fuzz/ssh_server_fuzzer.c
+++ b/tests/fuzz/ssh_server_fuzzer.c
@@ -139,6 +139,14 @@ int LLVMFuzzerTestOneInput(const uint8_t *data, size_t size)
         .channel_open_request_session_function = channel_open,
     };
 
+    /* This is the maximum that can be handled by the socket buffer before the
+     * other side will read some data. Other option would be feeding the socket
+     * from different thread which would not mind if it would be blocked, but I
+     * believe all the important inputs should fit into this size */
+    if (size > 219264) {
+        return -1;
+    }
+
     /* Write SSH RSA host key to disk */
     rc = write_rsa_hostkey("/tmp/libssh_fuzzer_private_key");
     assert(rc == 0);