diff --git a/include/mbedtls/ecdsa.h b/include/mbedtls/ecdsa.h
index a277715b3..b2587005f 100644
--- a/include/mbedtls/ecdsa.h
+++ b/include/mbedtls/ecdsa.h
@@ -219,8 +219,8 @@ int mbedtls_ecdsa_write_signature_det( mbedtls_ecdsa_context *ctx,
  *
  * \return          0 if successful,
  *                  MBEDTLS_ERR_ECP_BAD_INPUT_DATA if signature is invalid,
- *                  MBEDTLS_ERR_ECP_SIG_LEN_MISMATCH if the signature is
- *                  valid but its actual length is less than siglen,
+ *                  MBEDTLS_ERR_ECP_SIG_LEN_MISMATCH if there is a valid
+ *                  signature in sig but its length is less than siglen,
  *                  or a MBEDTLS_ERR_ECP_XXX or MBEDTLS_ERR_MPI_XXX error code
  */
 int mbedtls_ecdsa_read_signature( mbedtls_ecdsa_context *ctx,
diff --git a/include/mbedtls/ecp.h b/include/mbedtls/ecp.h
index ef6532633..3c2fbaa4b 100644
--- a/include/mbedtls/ecp.h
+++ b/include/mbedtls/ecp.h
@@ -35,7 +35,7 @@
 #define MBEDTLS_ERR_ECP_ALLOC_FAILED                      -0x4D80  /**< Memory allocation failed. */
 #define MBEDTLS_ERR_ECP_RANDOM_FAILED                     -0x4D00  /**< Generation of random value, such as (ephemeral) key, failed. */
 #define MBEDTLS_ERR_ECP_INVALID_KEY                       -0x4C80  /**< Invalid private or public key. */
-#define MBEDTLS_ERR_ECP_SIG_LEN_MISMATCH                  -0x4C00  /**< Signature is valid but shorter than the user-supplied length. */
+#define MBEDTLS_ERR_ECP_SIG_LEN_MISMATCH                  -0x4C00  /**< The buffer contains a valid signature followed by more data. */
 
 #ifdef __cplusplus
 extern "C" {
diff --git a/include/mbedtls/pk.h b/include/mbedtls/pk.h
index 458bb512a..3a6a1b335 100644
--- a/include/mbedtls/pk.h
+++ b/include/mbedtls/pk.h
@@ -62,7 +62,7 @@
 #define MBEDTLS_ERR_PK_INVALID_ALG         -0x3A80  /**< The algorithm tag or value is invalid. */
 #define MBEDTLS_ERR_PK_UNKNOWN_NAMED_CURVE -0x3A00  /**< Elliptic curve is unsupported (only NIST curves are supported). */
 #define MBEDTLS_ERR_PK_FEATURE_UNAVAILABLE -0x3980  /**< Unavailable feature, e.g. RSA disabled for RSA key. */
-#define MBEDTLS_ERR_PK_SIG_LEN_MISMATCH    -0x3900  /**< The signature is valid but its length is less than expected. */
+#define MBEDTLS_ERR_PK_SIG_LEN_MISMATCH    -0x3900  /**< The buffer contains a valid signature followed by more data. */
 
 #ifdef __cplusplus
 extern "C" {
@@ -267,8 +267,8 @@ int mbedtls_pk_can_do( const mbedtls_pk_context *ctx, mbedtls_pk_type_t type );
  * \param sig_len   Signature length
  *
  * \return          0 on success (signature is valid),
- *                  MBEDTLS_ERR_PK_SIG_LEN_MISMATCH if the signature is
- *                  valid but its actual length is less than sig_len,
+ *                  #MBEDTLS_ERR_PK_SIG_LEN_MISMATCH if there is a valid
+ *                  signature in sig but its length is less than \p siglen,
  *                  or a specific error code.
  *
  * \note            For RSA keys, the default padding type is PKCS#1 v1.5.
@@ -298,10 +298,10 @@ int mbedtls_pk_verify( mbedtls_pk_context *ctx, mbedtls_md_type_t md_alg,
  * \param sig_len   Signature length
  *
  * \return          0 on success (signature is valid),
- *                  MBEDTLS_ERR_PK_TYPE_MISMATCH if the PK context can't be
+ *                  #MBEDTLS_ERR_PK_TYPE_MISMATCH if the PK context can't be
  *                  used for this type of signatures,
- *                  MBEDTLS_ERR_PK_SIG_LEN_MISMATCH if the signature is
- *                  valid but its actual length is less than sig_len,
+ *                  #MBEDTLS_ERR_PK_SIG_LEN_MISMATCH if there is a valid
+ *                  signature in sig but its length is less than \p siglen,
  *                  or a specific error code.
  *
  * \note            If hash_len is 0, then the length associated with md_alg
diff --git a/library/ecdsa.c b/library/ecdsa.c
index 8892317bf..70fd20299 100644
--- a/library/ecdsa.c
+++ b/library/ecdsa.c
@@ -396,6 +396,9 @@ int mbedtls_ecdsa_read_signature( mbedtls_ecdsa_context *ctx,
                               &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 2c164b7df..23b41e738 100644
--- a/library/pk_wrap.c
+++ b/library/pk_wrap.c
@@ -90,6 +90,11 @@ static int rsa_verify_wrap( void *ctx, mbedtls_md_type_t md_alg,
                                   (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 );