diff --git a/src/modules/rtp/rtp-native.c b/src/modules/rtp/rtp-native.c
index 86760a627..d1a3911d7 100644
--- a/src/modules/rtp/rtp-native.c
+++ b/src/modules/rtp/rtp-native.c
@@ -200,7 +200,6 @@ int pa_rtp_recv(pa_rtp_context *c, pa_memchunk *chunk, pa_mempool *pool, uint32_
     uint32_t ssrc;
     uint8_t payload;
     unsigned cc;
-    ssize_t r;
     uint8_t aux[1024];
     bool found_tstamp = false;
 
@@ -209,6 +208,15 @@ int pa_rtp_recv(pa_rtp_context *c, pa_memchunk *chunk, pa_mempool *pool, uint32_
 
     pa_memchunk_reset(chunk);
 
+    /* FIONREAD works on both BSD and Linux, but they do something different:
+     * - on Linux it returns the amount of bytes in the next datagram
+     * - on BSDs it returns the total amount of bytes in the output buffer; this can be
+     *   more than one datagram and includes headers
+     *
+     * So the result will be a lower bound of how many bytes are needed, but might not be
+     * the exact size of the buffer size needed.
+     */
+
     if (ioctl(c->fd, FIONREAD, &size) < 0) {
         pa_log_warn("FIONREAD failed: %s", pa_cstrerror(errno));
         goto fail;
@@ -238,6 +246,9 @@ int pa_rtp_recv(pa_rtp_context *c, pa_memchunk *chunk, pa_mempool *pool, uint32_
         size = 1;
     }
 
+    /* Since size is a lower bound, also constrain it to an upper bound */
+    size = PA_MIN(size, 1<<16);
+
     if (c->recv_buf_size < (size_t) size) {
         do
             c->recv_buf_size *= 2;
@@ -259,12 +270,11 @@ int pa_rtp_recv(pa_rtp_context *c, pa_memchunk *chunk, pa_mempool *pool, uint32_
     m.msg_controllen = sizeof(aux);
     m.msg_flags = 0;
 
-    r = recvmsg(c->fd, &m, 0);
-
-    if (r != size) {
-        if (r < 0 && errno != EAGAIN && errno != EINTR)
-            pa_log_warn("recvmsg() failed: %s", r < 0 ? pa_cstrerror(errno) : "size mismatch");
+    size = recvmsg(c->fd, &m, 0);
 
+    if (size < 0) {
+        if (errno != EAGAIN && errno != EINTR)
+            pa_log_warn("recvmsg() failed: %s", pa_cstrerror(errno));
         goto fail;
     }
 
diff --git a/src/modules/rtp/sap.c b/src/modules/rtp/sap.c
index 8614022f8..00a648057 100644
--- a/src/modules/rtp/sap.c
+++ b/src/modules/rtp/sap.c
@@ -146,15 +146,25 @@ int pa_sap_recv(pa_sap_context *c, bool *goodbye) {
     char *buf = NULL, *e;
     uint32_t header;
     unsigned six, ac, k;
-    ssize_t r;
-
+ 
     pa_assert(c);
     pa_assert(goodbye);
 
+    /* FIONREAD works on both BSD and Linux, but they do something different:
+     * - on Linux it returns the amount of bytes in the next datagram
+     * - on BSDs it returns the total amount of bytes in the output buffer; this can be
+     *   more than one datagram and includes headers
+     *
+     * So the result will be a lower bound of how many bytes are needed, but might not be
+     * the exact size of the buffer size needed.
+     */
+
     if (ioctl(c->fd, FIONREAD, &size) < 0) {
         pa_log_warn("FIONREAD failed: %s", pa_cstrerror(errno));
         goto fail;
     }
+    /* Since size is a lower bound, also constrain it to an upper bound */
+    size = PA_MIN(size, 1<<16);
 
     buf = pa_xnew(char, (unsigned) size+1);
     buf[size] = 0;
@@ -170,8 +180,8 @@ int pa_sap_recv(pa_sap_context *c, bool *goodbye) {
     m.msg_controllen = 0;
     m.msg_flags = 0;
 
-    if ((r = recvmsg(c->fd, &m, 0)) != size) {
-        pa_log_warn("recvmsg() failed: %s", r < 0 ? pa_cstrerror(errno) : "size mismatch");
+    if ((size = recvmsg(c->fd, &m, 0)) < 0) {
+        pa_log_warn("recvmsg() failed: %s", pa_cstrerror(errno));
         goto fail;
     }