diff --git a/docs/about/deprecated.rst b/docs/about/deprecated.rst
index 35c8d7d1d4..ecccd5d3fc 100644
--- a/docs/about/deprecated.rst
+++ b/docs/about/deprecated.rst
@@ -496,3 +496,11 @@ devices or none.
 Please see "QMP invocation for live storage migration with
 ``blockdev-mirror`` + NBD" in docs/interop/live-block-operations.rst
 for a detailed explanation.
+
+old compression method (since 8.2)
+''''''''''''''''''''''''''''''''''
+
+Compression method fails too much.  Too many races.  We are going to
+remove it if nobody fixes it.  For starters, migration-test
+compression tests are disabled becase they fail randomly.  If you need
+compression, use multifd compression methods.
diff --git a/migration/options.c b/migration/options.c
index ae8ab47e32..9a39826ca5 100644
--- a/migration/options.c
+++ b/migration/options.c
@@ -483,6 +483,11 @@ bool migrate_caps_check(bool *old_caps, bool *new_caps, Error **errp)
                     " use blockdev-mirror with NBD instead");
     }
 
+    if (new_caps[MIGRATION_CAPABILITY_COMPRESS]) {
+        warn_report("old compression method is deprecated;"
+                    " use multifd compression methods instead");
+    }
+
 #ifndef CONFIG_REPLICATION
     if (new_caps[MIGRATION_CAPABILITY_X_COLO]) {
         error_setg(errp, "QEMU compiled without replication module"
@@ -1335,18 +1340,26 @@ static void migrate_params_apply(MigrateSetParameters *params, Error **errp)
     /* TODO use QAPI_CLONE() instead of duplicating it inline */
 
     if (params->has_compress_level) {
+        warn_report("old compression is deprecated;"
+                    " use multifd compression methods instead");
         s->parameters.compress_level = params->compress_level;
     }
 
     if (params->has_compress_threads) {
+        warn_report("old compression is deprecated;"
+                    " use multifd compression methods instead");
         s->parameters.compress_threads = params->compress_threads;
     }
 
     if (params->has_compress_wait_thread) {
+        warn_report("old compression is deprecated;"
+                    " use multifd compression methods instead");
         s->parameters.compress_wait_thread = params->compress_wait_thread;
     }
 
     if (params->has_decompress_threads) {
+        warn_report("old compression is deprecated;"
+                    " use multifd compression methods instead");
         s->parameters.decompress_threads = params->decompress_threads;
     }
 
diff --git a/qapi/migration.json b/qapi/migration.json
index e3b00a215b..e6610af428 100644
--- a/qapi/migration.json
+++ b/qapi/migration.json
@@ -272,6 +272,10 @@
 # Features:
 #
 # @deprecated: Member @disk is deprecated because block migration is.
+#     Member @compression is deprecated because it is unreliable and
+#     untested.  It is recommended to use multifd migration, which
+#     offers an alternative compression implementation that is
+#     reliable and tested.
 #
 # Since: 0.14
 ##
@@ -289,7 +293,7 @@
            '*blocked-reasons': ['str'],
            '*postcopy-blocktime': 'uint32',
            '*postcopy-vcpu-blocktime': ['uint32'],
-           '*compression': 'CompressionStats',
+           '*compression': { 'type': 'CompressionStats', 'features': [ 'deprecated' ] },
            '*socket-address': ['SocketAddress'],
            '*dirty-limit-throttle-time-per-round': 'uint64',
            '*dirty-limit-ring-full-time': 'uint64'} }
@@ -530,7 +534,10 @@
 # Features:
 #
 # @deprecated: Member @block is deprecated.  Use blockdev-mirror with
-#     NBD instead.
+#     NBD instead.  Member @compression is deprecated because it is
+#     unreliable and untested.  It is recommended to use multifd
+#     migration, which offers an alternative compression
+#     implementation that is reliable and tested.
 #
 # @unstable: Members @x-colo and @x-ignore-shared are experimental.
 #
@@ -538,7 +545,8 @@
 ##
 { 'enum': 'MigrationCapability',
   'data': ['xbzrle', 'rdma-pin-all', 'auto-converge', 'zero-blocks',
-           'compress', 'events', 'postcopy-ram',
+           { 'name': 'compress', 'features': [ 'deprecated' ] },
+           'events', 'postcopy-ram',
            { 'name': 'x-colo', 'features': [ 'unstable' ] },
            'release-ram',
            { 'name': 'block', 'features': [ 'deprecated' ] },
@@ -844,7 +852,9 @@
 # Features:
 #
 # @deprecated: Member @block-incremental is deprecated.  Use
-#     blockdev-mirror with NBD instead.
+#     blockdev-mirror with NBD instead.  Members @compress-level,
+#     @compress-threads, @decompress-threads and @compress-wait-thread
+#     are deprecated because @compression is deprecated.
 #
 # @unstable: Members @x-checkpoint-delay and @x-vcpu-dirty-limit-period
 #     are experimental.
@@ -854,8 +864,11 @@
 { 'enum': 'MigrationParameter',
   'data': ['announce-initial', 'announce-max',
            'announce-rounds', 'announce-step',
-           'compress-level', 'compress-threads', 'decompress-threads',
-           'compress-wait-thread', 'throttle-trigger-threshold',
+           { 'name': 'compress-level', 'features': [ 'deprecated' ] },
+           { 'name': 'compress-threads', 'features': [ 'deprecated' ] },
+           { 'name': 'decompress-threads', 'features': [ 'deprecated' ] },
+           { 'name': 'compress-wait-thread', 'features': [ 'deprecated' ] },
+           'throttle-trigger-threshold',
            'cpu-throttle-initial', 'cpu-throttle-increment',
            'cpu-throttle-tailslow',
            'tls-creds', 'tls-hostname', 'tls-authz', 'max-bandwidth',
@@ -1023,7 +1036,9 @@
 # Features:
 #
 # @deprecated: Member @block-incremental is deprecated.  Use
-#     blockdev-mirror with NBD instead.
+#     blockdev-mirror with NBD instead.  Members @compress-level,
+#     @compress-threads, @decompress-threads and @compress-wait-thread
+#     are deprecated because @compression is deprecated.
 #
 # @unstable: Members @x-checkpoint-delay and @x-vcpu-dirty-limit-period
 #     are experimental.
@@ -1038,10 +1053,14 @@
             '*announce-max': 'size',
             '*announce-rounds': 'size',
             '*announce-step': 'size',
-            '*compress-level': 'uint8',
-            '*compress-threads': 'uint8',
-            '*compress-wait-thread': 'bool',
-            '*decompress-threads': 'uint8',
+            '*compress-level': { 'type': 'uint8',
+                                 'features': [ 'deprecated' ] },
+            '*compress-threads':  { 'type': 'uint8',
+                                    'features': [ 'deprecated' ] },
+            '*compress-wait-thread':  { 'type': 'bool',
+                                        'features': [ 'deprecated' ] },
+            '*decompress-threads':  { 'type': 'uint8',
+                                      'features': [ 'deprecated' ] },
             '*throttle-trigger-threshold': 'uint8',
             '*cpu-throttle-initial': 'uint8',
             '*cpu-throttle-increment': 'uint8',
@@ -1078,7 +1097,7 @@
 # Example:
 #
 # -> { "execute": "migrate-set-parameters" ,
-#      "arguments": { "compress-level": 1 } }
+#      "arguments": { "multifd-channels": 5 } }
 # <- { "return": {} }
 ##
 { 'command': 'migrate-set-parameters', 'boxed': true,
@@ -1241,7 +1260,9 @@
 # Features:
 #
 # @deprecated: Member @block-incremental is deprecated.  Use
-#     blockdev-mirror with NBD instead.
+#     blockdev-mirror with NBD instead.  Members @compress-level,
+#     @compress-threads, @decompress-threads and @compress-wait-thread
+#     are deprecated because @compression is deprecated.
 #
 # @unstable: Members @x-checkpoint-delay and @x-vcpu-dirty-limit-period
 #     are experimental.
@@ -1253,10 +1274,14 @@
             '*announce-max': 'size',
             '*announce-rounds': 'size',
             '*announce-step': 'size',
-            '*compress-level': 'uint8',
-            '*compress-threads': 'uint8',
-            '*compress-wait-thread': 'bool',
-            '*decompress-threads': 'uint8',
+            '*compress-level': { 'type': 'uint8',
+                                 'features': [ 'deprecated' ] },
+            '*compress-threads': { 'type': 'uint8',
+                                   'features': [ 'deprecated' ] },
+            '*compress-wait-thread': { 'type': 'bool',
+                                       'features': [ 'deprecated' ] },
+            '*decompress-threads': { 'type': 'uint8',
+                                     'features': [ 'deprecated' ] },
             '*throttle-trigger-threshold': 'uint8',
             '*cpu-throttle-initial': 'uint8',
             '*cpu-throttle-increment': 'uint8',
@@ -1296,10 +1321,8 @@
 #
 # -> { "execute": "query-migrate-parameters" }
 # <- { "return": {
-#          "decompress-threads": 2,
+#          "multifd-channels": 2,
 #          "cpu-throttle-increment": 10,
-#          "compress-threads": 8,
-#          "compress-level": 1,
 #          "cpu-throttle-initial": 20,
 #          "max-bandwidth": 33554432,
 #          "downtime-limit": 300