diff --git a/dev/update-alloc-limits-to-last-completed-ci-build b/dev/update-alloc-limits-to-last-completed-ci-build
index e96c743e..f639b776 100755
--- a/dev/update-alloc-limits-to-last-completed-ci-build
+++ b/dev/update-alloc-limits-to-last-completed-ci-build
@@ -22,7 +22,7 @@ url_prefix=${1-"https://ci.swiftserver.group/job/swift-nio-http2-2-"}
 target_repo=${2-"$here/.."}
 tmpdir=$(mktemp -d /tmp/.last-build_XXXXXX)
 
-for f in swift52 swift53 swift54 swift55 nightly; do
+for f in swift52 swift53 swift54 swift55 swift56 nightly; do
     echo "$f"
     url="$url_prefix$f-prb/lastCompletedBuild/consoleFull"
     stripped=${f#"swift"}
diff --git a/docker/docker-compose.1604.52.yaml b/docker/docker-compose.1604.52.yaml
index 7cf7b20b..1e83cf34 100644
--- a/docker/docker-compose.1604.52.yaml
+++ b/docker/docker-compose.1604.52.yaml
@@ -25,17 +25,17 @@ services:
   test:
     image: swift-nio-http2:16.04-5.2
     environment:
-      - MAX_ALLOCS_ALLOWED_1k_requests_interleaved=51150
-      - MAX_ALLOCS_ALLOWED_1k_requests_noninterleaved=50100
-      - MAX_ALLOCS_ALLOWED_client_server_h1_request_response=324900
-      - MAX_ALLOCS_ALLOWED_client_server_request_response=288900
-      - MAX_ALLOCS_ALLOWED_create_client_stream_channel=48050
+      - MAX_ALLOCS_ALLOWED_1k_requests_interleaved=48200
+      - MAX_ALLOCS_ALLOWED_1k_requests_noninterleaved=47100
+      - MAX_ALLOCS_ALLOWED_client_server_h1_request_response=311050
+      - MAX_ALLOCS_ALLOWED_client_server_request_response=275050
+      - MAX_ALLOCS_ALLOWED_create_client_stream_channel=42050
       - MAX_ALLOCS_ALLOWED_get_100000_headers_canonical_form=200050
       - MAX_ALLOCS_ALLOWED_get_100000_headers_canonical_form_trimming_whitespace=200050
       - MAX_ALLOCS_ALLOWED_get_100000_headers_canonical_form_trimming_whitespace_from_long_string=300050
       - MAX_ALLOCS_ALLOWED_get_100000_headers_canonical_form_trimming_whitespace_from_short_string=200050
       - MAX_ALLOCS_ALLOWED_hpack_decoding=5050
-      - MAX_ALLOCS_ALLOWED_stream_teardown_100_concurrent=353200
+      - MAX_ALLOCS_ALLOWED_stream_teardown_100_concurrent=323250
       - SANITIZER_ARG=--sanitize=thread
 
   shell:
diff --git a/docker/docker-compose.1804.53.yaml b/docker/docker-compose.1804.53.yaml
index d029eaf2..c0104d1f 100644
--- a/docker/docker-compose.1804.53.yaml
+++ b/docker/docker-compose.1804.53.yaml
@@ -25,17 +25,17 @@ services:
   test:
     image: swift-nio-http2:18.04-5.3
     environment:
-      - MAX_ALLOCS_ALLOWED_1k_requests_interleaved=49150
-      - MAX_ALLOCS_ALLOWED_1k_requests_noninterleaved=48100
-      - MAX_ALLOCS_ALLOWED_client_server_h1_request_response=324000
-      - MAX_ALLOCS_ALLOWED_client_server_request_response=288000
-      - MAX_ALLOCS_ALLOWED_create_client_stream_channel=48050
+      - MAX_ALLOCS_ALLOWED_1k_requests_interleaved=46200
+      - MAX_ALLOCS_ALLOWED_1k_requests_noninterleaved=45100
+      - MAX_ALLOCS_ALLOWED_client_server_h1_request_response=310050
+      - MAX_ALLOCS_ALLOWED_client_server_request_response=274050
+      - MAX_ALLOCS_ALLOWED_create_client_stream_channel=42050
       - MAX_ALLOCS_ALLOWED_get_100000_headers_canonical_form=200050
       - MAX_ALLOCS_ALLOWED_get_100000_headers_canonical_form_trimming_whitespace=200050
       - MAX_ALLOCS_ALLOWED_get_100000_headers_canonical_form_trimming_whitespace_from_long_string=300050
       - MAX_ALLOCS_ALLOWED_get_100000_headers_canonical_form_trimming_whitespace_from_short_string=200050
       - MAX_ALLOCS_ALLOWED_hpack_decoding=5050
-      - MAX_ALLOCS_ALLOWED_stream_teardown_100_concurrent=333200
+      - MAX_ALLOCS_ALLOWED_stream_teardown_100_concurrent=303250
 
   shell:
     image: swift-nio-http2:18.04-5.3
diff --git a/docker/docker-compose.2004.54.yaml b/docker/docker-compose.2004.54.yaml
index 471c8442..00b2ebde 100644
--- a/docker/docker-compose.2004.54.yaml
+++ b/docker/docker-compose.2004.54.yaml
@@ -26,17 +26,17 @@ services:
   test:
     image: swift-nio-http2:20.04-5.4
     environment:
-      - MAX_ALLOCS_ALLOWED_1k_requests_interleaved=49150
-      - MAX_ALLOCS_ALLOWED_1k_requests_noninterleaved=48100
-      - MAX_ALLOCS_ALLOWED_client_server_h1_request_response=324000
-      - MAX_ALLOCS_ALLOWED_client_server_request_response=288000
-      - MAX_ALLOCS_ALLOWED_create_client_stream_channel=48050
+      - MAX_ALLOCS_ALLOWED_1k_requests_interleaved=46200
+      - MAX_ALLOCS_ALLOWED_1k_requests_noninterleaved=45100
+      - MAX_ALLOCS_ALLOWED_client_server_h1_request_response=310050
+      - MAX_ALLOCS_ALLOWED_client_server_request_response=274050
+      - MAX_ALLOCS_ALLOWED_create_client_stream_channel=42050
       - MAX_ALLOCS_ALLOWED_get_100000_headers_canonical_form=200050
       - MAX_ALLOCS_ALLOWED_get_100000_headers_canonical_form_trimming_whitespace=200050
       - MAX_ALLOCS_ALLOWED_get_100000_headers_canonical_form_trimming_whitespace_from_long_string=300050
       - MAX_ALLOCS_ALLOWED_get_100000_headers_canonical_form_trimming_whitespace_from_short_string=200050
       - MAX_ALLOCS_ALLOWED_hpack_decoding=5050
-      - MAX_ALLOCS_ALLOWED_stream_teardown_100_concurrent=333200
+      - MAX_ALLOCS_ALLOWED_stream_teardown_100_concurrent=303250
 
   shell:
     image: swift-nio-http2:20.04-5.4
diff --git a/docker/docker-compose.2004.55.yaml b/docker/docker-compose.2004.55.yaml
index 92b77545..fd18a6d6 100644
--- a/docker/docker-compose.2004.55.yaml
+++ b/docker/docker-compose.2004.55.yaml
@@ -25,17 +25,17 @@ services:
   test:
     image: swift-nio-http2:20.04-5.5
     environment:
-      - MAX_ALLOCS_ALLOWED_1k_requests_interleaved=49150
-      - MAX_ALLOCS_ALLOWED_1k_requests_noninterleaved=48100
-      - MAX_ALLOCS_ALLOWED_client_server_h1_request_response=324000
-      - MAX_ALLOCS_ALLOWED_client_server_request_response=288000
-      - MAX_ALLOCS_ALLOWED_create_client_stream_channel=48050
+      - MAX_ALLOCS_ALLOWED_1k_requests_interleaved=46200
+      - MAX_ALLOCS_ALLOWED_1k_requests_noninterleaved=45100
+      - MAX_ALLOCS_ALLOWED_client_server_h1_request_response=310050
+      - MAX_ALLOCS_ALLOWED_client_server_request_response=274050
+      - MAX_ALLOCS_ALLOWED_create_client_stream_channel=42050
       - MAX_ALLOCS_ALLOWED_get_100000_headers_canonical_form=200050
       - MAX_ALLOCS_ALLOWED_get_100000_headers_canonical_form_trimming_whitespace=200050
       - MAX_ALLOCS_ALLOWED_get_100000_headers_canonical_form_trimming_whitespace_from_long_string=300050
       - MAX_ALLOCS_ALLOWED_get_100000_headers_canonical_form_trimming_whitespace_from_short_string=200050
       - MAX_ALLOCS_ALLOWED_hpack_decoding=5050
-      - MAX_ALLOCS_ALLOWED_stream_teardown_100_concurrent=333150
+      - MAX_ALLOCS_ALLOWED_stream_teardown_100_concurrent=303250
 
   shell:
     image: swift-nio-http2:20.04-5.5
diff --git a/docker/docker-compose.2004.56.yaml b/docker/docker-compose.2004.56.yaml
new file mode 100644
index 00000000..5333d6a0
--- /dev/null
+++ b/docker/docker-compose.2004.56.yaml
@@ -0,0 +1,41 @@
+version: "3"
+
+services:
+
+  runtime-setup:
+    image: swift-nio-http2:20.04-5.6
+    build:
+      args:
+        base_image: "swiftlang/swift:nightly-5.6-focal"
+        ubuntu_version: "focal"
+        h2spec_version: "2.2.1"
+
+  unit-tests:
+    image: swift-nio-http2:20.04-5.6
+
+  integration-tests:
+    image: swift-nio-http2:20.04-5.6
+
+  performance-test:
+    image: swift-nio-http2:20.04-5.6
+
+  h2spec:
+    image: swift-nio-http2:20.04-5.6
+
+  test:
+    image: swift-nio-http2:20.04-5.6
+    environment:
+      - MAX_ALLOCS_ALLOWED_1k_requests_interleaved=43200
+      - MAX_ALLOCS_ALLOWED_1k_requests_noninterleaved=42100
+      - MAX_ALLOCS_ALLOWED_client_server_h1_request_response=304050
+      - MAX_ALLOCS_ALLOWED_client_server_request_response=270050
+      - MAX_ALLOCS_ALLOWED_create_client_stream_channel=41050
+      - MAX_ALLOCS_ALLOWED_get_100000_headers_canonical_form=200050
+      - MAX_ALLOCS_ALLOWED_get_100000_headers_canonical_form_trimming_whitespace=200050
+      - MAX_ALLOCS_ALLOWED_get_100000_headers_canonical_form_trimming_whitespace_from_long_string=300050
+      - MAX_ALLOCS_ALLOWED_get_100000_headers_canonical_form_trimming_whitespace_from_short_string=200050
+      - MAX_ALLOCS_ALLOWED_hpack_decoding=5050
+      - MAX_ALLOCS_ALLOWED_stream_teardown_100_concurrent=293250
+
+  shell:
+    image: swift-nio-http2:20.04-5.6
diff --git a/docker/docker-compose.2004.main.yaml b/docker/docker-compose.2004.main.yaml
index c58dfe79..868aac39 100644
--- a/docker/docker-compose.2004.main.yaml
+++ b/docker/docker-compose.2004.main.yaml
@@ -25,17 +25,17 @@ services:
   test:
     image: swift-nio-http2:20.04-main
     environment:
-      - MAX_ALLOCS_ALLOWED_1k_requests_interleaved=46150
-      - MAX_ALLOCS_ALLOWED_1k_requests_noninterleaved=45100
-      - MAX_ALLOCS_ALLOWED_client_server_h1_request_response=317250
-      - MAX_ALLOCS_ALLOWED_client_server_request_response=284000
-      - MAX_ALLOCS_ALLOWED_create_client_stream_channel=47050
+      - MAX_ALLOCS_ALLOWED_1k_requests_interleaved=43200
+      - MAX_ALLOCS_ALLOWED_1k_requests_noninterleaved=42100
+      - MAX_ALLOCS_ALLOWED_client_server_h1_request_response=304050
+      - MAX_ALLOCS_ALLOWED_client_server_request_response=270050
+      - MAX_ALLOCS_ALLOWED_create_client_stream_channel=41050
       - MAX_ALLOCS_ALLOWED_get_100000_headers_canonical_form=200050
       - MAX_ALLOCS_ALLOWED_get_100000_headers_canonical_form_trimming_whitespace=200050
       - MAX_ALLOCS_ALLOWED_get_100000_headers_canonical_form_trimming_whitespace_from_long_string=300050
       - MAX_ALLOCS_ALLOWED_get_100000_headers_canonical_form_trimming_whitespace_from_short_string=200050
       - MAX_ALLOCS_ALLOWED_hpack_decoding=5050
-      - MAX_ALLOCS_ALLOWED_stream_teardown_100_concurrent=323200
+      - MAX_ALLOCS_ALLOWED_stream_teardown_100_concurrent=293250
 
   shell:
     image: swift-nio-http2:20.04-main