diff --git a/library/ecdsa.c b/library/ecdsa.c
index 8892317..70fd202 100644
--- a/library/ecdsa.c
+++ b/library/ecdsa.c
@@ -396,6 +396,9 @@
                               &ctx->Q, &r, &s ) ) != 0 )
         goto cleanup;
 
+    /* At this point we know that the buffer starts with a valid signature.
+     * Return 0 if the buffer just contains the signature, and a specific
+     * error code if the valid signature is followed by more data. */
     if( p != end )
         ret = MBEDTLS_ERR_ECP_SIG_LEN_MISMATCH;
 
diff --git a/library/pk_wrap.c b/library/pk_wrap.c
index 2c164b7..23b41e7 100644
--- a/library/pk_wrap.c
+++ b/library/pk_wrap.c
@@ -90,6 +90,11 @@
                                   (unsigned int) hash_len, hash, sig ) ) != 0 )
         return( ret );
 
+    /* The buffer contains a valid signature followed by extra data.
+     * We have a special error code for that so that so that callers can
+     * use mbedtls_pk_verify() to check "Does the buffer start with a
+     * valid signature?" and not just "Does the buffer contain a valid
+     * signature?". */
     if( sig_len > ((mbedtls_rsa_context *) ctx)->len )
         return( MBEDTLS_ERR_PK_SIG_LEN_MISMATCH );