diff --git a/src/src/auths/cram_md5.c b/src/src/auths/cram_md5.c
index 44b05465cf..6274780dd5 100644
--- a/src/src/auths/cram_md5.c
+++ b/src/src/auths/cram_md5.c
@@ -238,15 +238,21 @@ HDEBUG(D_auth)
 
 /* We now have to compare the digest, which is 16 bytes in binary, with the
 data received, which is expressed in lower case hex. We checked above that
-there were 32 characters of data left. */
+there were 32 characters of data left. Use constant-time comparison to
+prevent timing side-channel. */
 
-for (i = 0; i < 16; i++)
-  {
-  int a = *clear++;
-  int b = *clear++;
-  if (((((a >= 'a')? a - 'a' + 10 : a - '0') << 4) +
-        ((b >= 'a')? b - 'a' + 10 : b - '0')) != digest[i]) return FAIL;
-  }
+{
+  volatile unsigned char result = 0;
+  for (i = 0; i < 16; i++)
+    {
+    int a = *clear++;
+    int b = *clear++;
+    unsigned char hex_val = (((a >= 'a')? a - 'a' + 10 : a - '0') << 4) +
+                             ((b >= 'a')? b - 'a' + 10 : b - '0');
+    result |= hex_val ^ digest[i];
+    }
+  if (result != 0) return FAIL;
+}
 
 /* Expand server_condition as an authorization check */
 return auth_check_serv_cond(ablock);
diff --git a/src/src/auths/spa.c b/src/src/auths/spa.c
index 3e2cccde9d..12e63d8af2 100644
--- a/src/src/auths/spa.c
+++ b/src/src/auths/spa.c
@@ -260,8 +260,14 @@ if (off >= sizeof(SPAAuthResponse) - 24)
   }
 s = (US responseptr) + off;
 
-if (memcmp(ntRespData, s, 24) == 0)
-  return auth_check_serv_cond(ablock);	/* success. we have a winner. */
+/* Use constant-time comparison to prevent timing side-channel */
+{
+  volatile unsigned char result = 0;
+  for (int i = 0; i < 24; i++)
+    result |= ntRespData[i] ^ s[i];
+  if (result == 0)
+    return auth_check_serv_cond(ablock);	/* success. we have a winner. */
+}
 
   /* Expand server_condition as an authorization check (PH) */
 
diff --git a/src/src/mime.c b/src/src/mime.c
index 0197894dab..da48325f33 100644
--- a/src/src/mime.c
+++ b/src/src/mime.c
@@ -496,6 +496,21 @@ int rc = OK;
 uschar * header = NULL;
 struct mime_boundary_context nested_context;
 
+/* Limit MIME nesting depth to prevent stack overflow from crafted messages.
+RFC 2046 does not specify a maximum, but 100 levels is far beyond any
+legitimate use. */
+
+  {
+  int depth = 0;
+  for (struct mime_boundary_context *p = context; p; p = p->parent)
+    if (++depth > 100)
+      {
+      log_write(0, LOG_MAIN,
+	"MIME: nesting depth limit (100) exceeded, skipping");
+      return OK;
+      }
+  }
+
 /* reserve a line buffer to work in.  Assume tainted data. */
 header = store_get(MIME_MAX_HEADER_SIZE+1, GET_TAINTED);
 
diff --git a/src/src/receive.c b/src/src/receive.c
index f1833c5a09..dc518e0f7b 100644
--- a/src/src/receive.c
+++ b/src/src/receive.c
@@ -1095,7 +1095,7 @@ for (;;)
   {
   if (chunking_data_left > 0)
     {
-    unsigned len = MAX(chunking_data_left, thismessage_size_limit - message_size + 1);
+    unsigned len = MIN(chunking_data_left, thismessage_size_limit - message_size + 1);
     const uschar * buf = bdat_getbuf(&len);
 
     if (!buf) return END_EOF;