diff --git a/include/mbedtls/ssl.h b/include/mbedtls/ssl.h
index 9b17e61..6460fd9 100644
--- a/include/mbedtls/ssl.h
+++ b/include/mbedtls/ssl.h
@@ -579,6 +579,21 @@
  *                  store an operation context for later retrieval
  *                  by the resume callback.
  *
+ * \note            For RSA signatures, this function must produce output
+ *                  that is consistent with PKCS#1 v1.5 in the same way as
+ *                  mbedtls_rsa_pkcs1_sign(). Before the private key operation,
+ *                  apply the padding steps described in RFC 8017, section 9.2
+ *                  "EMSA-PKCS1-v1_5" as follows.
+ *                  - If \p md_alg is #MBEDTLS_MD_NONE, apply the PKCS#1 v1.5
+ *                    encoding, treating \p hash as the DigestInfo to be
+ *                    padded. In other words, apply EMSA-PKCS1-v1_5 starting
+ *                    from step 3, with `T = hash` and `tLen = hash_len`.
+ *                  - If \p md_alg is #MBEDTLS_MD_NONE, apply the PKCS#1 v1.5
+ *                    encoding, treating \p hash as the hash to be encoded and
+ *                    padded. In other words, apply EMSA-PKCS1-v1_5 starting
+ *                    from step 2, with `digestAlgorithm` obtained by calling
+ *                    mbedtls_oid_get_oid_by_md() on \p md_alg.
+ *
  * \param config_data     The configuration data parameter passed to
  *                        mbedtls_ssl_conf_async_private_cb().
  * \param ssl             The SSL connection instance. It should not be
diff --git a/programs/ssl/ssl_server2.c b/programs/ssl/ssl_server2.c
index 500ff04..28d9e6f 100644
--- a/programs/ssl/ssl_server2.c
+++ b/programs/ssl/ssl_server2.c
@@ -900,9 +900,25 @@
 }
 
 #define SSL_ASYNC_INPUT_MAX_SIZE 512
+
+typedef enum
+{
+    ASYNC_OP_SIGN,
+    ASYNC_OP_DECRYPT,
+} ssl_async_operation_type_t;
+/* Note that the enum above and the array below need to be kept in sync!
+ * `ssl_async_operation_names[op]` is the name of op for each value `op`
+ * of type `ssl_async_operation_type_t`. */
+static const char *const ssl_async_operation_names[] =
+{
+    "sign",
+    "decrypt",
+};
+
 typedef struct
 {
     size_t slot;
+    ssl_async_operation_type_t operation_type;
     mbedtls_md_type_t md_alg;
     unsigned char input[SSL_ASYNC_INPUT_MAX_SIZE];
     size_t input_len;
@@ -912,7 +928,7 @@
 static int ssl_async_start( void *config_data_arg,
                             mbedtls_ssl_context *ssl,
                             mbedtls_x509_crt *cert,
-                            const char *op_name,
+                            ssl_async_operation_type_t op_type,
                             mbedtls_md_type_t md_alg,
                             const unsigned char *input,
                             size_t input_len )
@@ -920,6 +936,7 @@
     ssl_async_key_context_t *config_data = config_data_arg;
     size_t slot;
     ssl_async_operation_context_t *ctx = NULL;
+    const char *op_name = ssl_async_operation_names[op_type];
 
     {
         char dn[100];
@@ -954,6 +971,7 @@
     if( ctx == NULL )
         return( MBEDTLS_ERR_SSL_ALLOC_FAILED );
     ctx->slot = slot;
+    ctx->operation_type = op_type;
     ctx->md_alg = md_alg;
     memcpy( ctx->input, input, input_len );
     ctx->input_len = input_len;
@@ -974,7 +992,7 @@
                            size_t hash_len )
 {
     return( ssl_async_start( config_data_arg, ssl, cert,
-                             "sign", md_alg,
+                             ASYNC_OP_SIGN, md_alg,
                              hash, hash_len ) );
 }
 
@@ -985,7 +1003,7 @@
                               size_t input_len )
 {
     return( ssl_async_start( config_data_arg, ssl, cert,
-                             "decrypt", MBEDTLS_MD_NONE,
+                             ASYNC_OP_DECRYPT, MBEDTLS_MD_NONE,
                              input, input_len ) );
 }
 
@@ -999,7 +1017,7 @@
     ssl_async_key_context_t *config_data = config_data_arg;
     ssl_async_key_slot_t *key_slot = &config_data->slots[ctx->slot];
     int ret;
-    const char *op_name;
+    const char *op_name = NULL;
 
     if( config_data->inject_error == SSL_ASYNC_INJECT_ERROR_RESUME )
     {
@@ -1015,22 +1033,28 @@
         return( MBEDTLS_ERR_SSL_ASYNC_IN_PROGRESS );
     }
 
-    if( ctx->md_alg == MBEDTLS_MD_NONE )
+    switch( ctx->operation_type )
     {
-        op_name = "decrypt";
-        ret = mbedtls_pk_decrypt( key_slot->pk,
-                                  ctx->input, ctx->input_len,
-                                  output, output_len, output_size,
-                                  config_data->f_rng, config_data->p_rng );
-    }
-    else
-    {
-        op_name = "sign";
-        ret = mbedtls_pk_sign( key_slot->pk,
-                               ctx->md_alg,
-                               ctx->input, ctx->input_len,
-                               output, output_len,
-                               config_data->f_rng, config_data->p_rng );
+        case ASYNC_OP_DECRYPT:
+            op_name = "decrypt";
+            ret = mbedtls_pk_decrypt( key_slot->pk,
+                                      ctx->input, ctx->input_len,
+                                      output, output_len, output_size,
+                                      config_data->f_rng, config_data->p_rng );
+            break;
+        case ASYNC_OP_SIGN:
+            op_name = "sign";
+            ret = mbedtls_pk_sign( key_slot->pk,
+                                   ctx->md_alg,
+                                   ctx->input, ctx->input_len,
+                                   output, output_len,
+                                   config_data->f_rng, config_data->p_rng );
+            break;
+        default:
+            mbedtls_printf( "Async resume (slot %zd): unknown operation type %ld. This shouldn't happen.\n",
+                            ctx->slot, (long) ctx->operation_type );
+            return( MBEDTLS_ERR_PK_FEATURE_UNAVAILABLE );
+            break;
     }
 
     if( config_data->inject_error == SSL_ASYNC_INJECT_ERROR_PK )
diff --git a/tests/ssl-opt.sh b/tests/ssl-opt.sh
index 15503e2..0f8af02 100755
--- a/tests/ssl-opt.sh
+++ b/tests/ssl-opt.sh
@@ -4088,6 +4088,18 @@
             -s "Async resume (slot [0-9]): call 0 more times." \
             -s "Async resume (slot [0-9]): sign done, status=0"
 
+# Test that the async callback correctly signs the 36-byte hash of TLS 1.0/1.1
+# with RSA PKCS#1v1.5 as used in TLS 1.0/1.1.
+requires_config_enabled MBEDTLS_SSL_ASYNC_PRIVATE
+requires_config_enabled MBEDTLS_SSL_PROTO_TLS1_1
+run_test    "SSL async private: sign, RSA, TLS 1.1" \
+            "$P_SRV key_file=data_files/server2.key crt_file=data_files/server2.crt \
+             async_operations=s async_private_delay1=0 async_private_delay2=0" \
+            "$P_CLI force_version=tls1_1" \
+            0 \
+            -s "Async sign callback: using key slot " \
+            -s "Async resume (slot [0-9]): sign done, status=0"
+
 requires_config_enabled MBEDTLS_SSL_ASYNC_PRIVATE
 run_test    "SSL async private: decrypt, delay=0" \
             "$P_SRV \