diff --git a/.github/workflows/CI.yml b/.github/workflows/CI.yml
index 359c6003..4e796d37 100644
--- a/.github/workflows/CI.yml
+++ b/.github/workflows/CI.yml
@@ -2,7 +2,7 @@ name: CI
 
 env:
   CARGO_TERM_COLOR: always
-  MSRV: 1.56.0
+  MSRV: 1.56
 
 on:
   push:
@@ -113,6 +113,12 @@ jobs:
         command: update
         args: -Z minimal-versions
         toolchain: nightly
+    - name: Fix up Cargo.lock
+      uses: actions-rs/cargo@v1
+      with:
+        command: update
+        args: -p crc32fast --precise 1.1.1
+        toolchain: nightly
     - name: Run tests
       uses: actions-rs/cargo@v1
       with:
@@ -121,7 +127,6 @@ jobs:
           -p axum
           -p axum-extra
           -p axum-core
-          -p internal-minimal-versions
           --all-features
           --all-targets
           --locked
@@ -135,7 +140,6 @@ jobs:
         command: test
         args: >
           -p axum-macros
-          -p internal-minimal-versions
           --doc
           --all-features
           --locked
diff --git a/Cargo.toml b/Cargo.toml
index a221fbc5..7853fc3e 100644
--- a/Cargo.toml
+++ b/Cargo.toml
@@ -4,9 +4,5 @@ members = [
     "axum-core",
     "axum-extra",
     "axum-macros",
-
-    # internal crate used to bump the minimum versions we
-    # get for some dependencies which otherwise wouldn't build
-    # with `cargo +nightly update -Z minimal-versions`
-    "internal-minimal-versions",
 ]
+resolver = "2"
diff --git a/axum/Cargo.toml b/axum/Cargo.toml
index 20f7178a..4aeac8bb 100644
--- a/axum/Cargo.toml
+++ b/axum/Cargo.toml
@@ -25,6 +25,9 @@ query = ["serde_urlencoded"]
 tower-log = ["tower/log"]
 ws = ["tokio-tungstenite", "sha-1", "base64"]
 
+# Required for intra-doc links to resolve correctly
+__private_docs = ["tower/full", "tower-http/full"]
+
 [dependencies]
 async-trait = "0.1.43"
 axum-core = { path = "../axum-core", version = "0.2.6" }
@@ -43,7 +46,7 @@ pin-project-lite = "0.2.7"
 serde = "1.0"
 sync_wrapper = "0.1.1"
 tokio = { version = "1", features = ["time"] }
-tower = { version = "0.4.11", default-features = false, features = ["util", "make"] }
+tower = { version = "0.4.13", default-features = false, features = ["util", "make"] }
 tower-http = { version = "0.3.0", features = ["util", "map-response-body"] }
 tower-layer = "0.3"
 tower-service = "0.3"
@@ -56,7 +59,7 @@ multer = { version = "2.0.0", optional = true }
 serde_json = { version = "1.0", features = ["raw_value"], optional = true }
 serde_urlencoded = { version = "0.7", optional = true }
 sha-1 = { version = "0.10", optional = true }
-tokio-tungstenite = { version = "0.17", optional = true }
+tokio-tungstenite = { version = "0.17.2", optional = true }
 
 [dev-dependencies]
 anyhow = "1.0"
diff --git a/examples/Cargo.toml b/examples/Cargo.toml
index 4f10fc34..66964292 100644
--- a/examples/Cargo.toml
+++ b/examples/Cargo.toml
@@ -1,3 +1,4 @@
 [workspace]
 members = ["*"]
 exclude = ["target"]
+resolver = "2"
diff --git a/internal-minimal-versions/Cargo.toml b/internal-minimal-versions/Cargo.toml
deleted file mode 100644
index 9e2a69c7..00000000
--- a/internal-minimal-versions/Cargo.toml
+++ /dev/null
@@ -1,16 +0,0 @@
-[package]
-name = "internal-minimal-versions"
-version = "0.1.0"
-edition = "2021"
-publish = false
-
-# these dependencies don't build if installed with `cargo +nightly update -Z
-# minimal-versions` so we add them here to make sure we get a version that
-# does build
-#
-# this only matters for axum's CI
-[dependencies]
-crc32fast = "1.3.2"
-gcc = "0.3.55"
-time = "0.3.9"
-tungstenite = "0.17.2"
diff --git a/internal-minimal-versions/src/lib.rs b/internal-minimal-versions/src/lib.rs
deleted file mode 100644
index 36db4933..00000000
--- a/internal-minimal-versions/src/lib.rs
+++ /dev/null
@@ -1 +0,0 @@
-// intentionally left empty