diff --git a/.github/workflows/build.yml b/.github/workflows/build.yml
index 474cadda8c3..2ff3edf35b3 100644
--- a/.github/workflows/build.yml
+++ b/.github/workflows/build.yml
@@ -57,7 +57,7 @@ jobs:
       - name: Run CI script
         if: "!matrix.coverage"
         shell: bash # Default on Winblows is powershell
-        run: ./ci/ci-tests.sh
+        run: CI_MINIMIZE_DISK_USAGE=1 ./ci/ci-tests.sh
       - name: Install deps for kcov
         if: matrix.coverage
         run: |
diff --git a/ci/ci-tests.sh b/ci/ci-tests.sh
index 7a16b749200..dc52d0e6e9d 100755
--- a/ci/ci-tests.sh
+++ b/ci/ci-tests.sh
@@ -29,11 +29,20 @@ PIN_RELEASE_DEPS # pin the release dependencies in our main workspace
 # The quote crate switched to Rust edition 2021 starting with v1.0.31, i.e., has MSRV of 1.56
 [ "$RUSTC_MINOR_VERSION" -lt 56 ] && cargo update -p quote --precise "1.0.30" --verbose
 
+# The syn crate depends on too-new proc-macro2 starting with v2.0.33, i.e., has MSRV of 1.56
+if [ "$RUSTC_MINOR_VERSION" -lt 56 ]; then
+	SYN_2_DEP=$(grep -o '"syn 2.*' Cargo.lock | tr -d '",' | tr ' ' ':')
+	cargo update -p "$SYN_2_DEP" --precise "2.0.32" --verbose
+fi
+
 # The proc-macro2 crate switched to Rust edition 2021 starting with v1.0.66, i.e., has MSRV of 1.56
 [ "$RUSTC_MINOR_VERSION" -lt 56 ] && cargo update -p proc-macro2 --precise "1.0.65" --verbose
 
 [ "$LDK_COVERAGE_BUILD" != "" ] && export RUSTFLAGS="-C link-dead-code"
 
+# The memchr crate switched to an MSRV of 1.60 starting with v2.6.0
+[ "$RUSTC_MINOR_VERSION" -lt 60 ] && cargo update -p memchr --precise "2.5.0" --verbose
+
 export RUST_BACKTRACE=1
 
 echo -e "\n\nBuilding and testing all workspace crates..."
@@ -81,13 +90,20 @@ if [[ $RUSTC_MINOR_VERSION -gt 67 ]]; then
 	# lightning-transaction-sync's MSRV is 1.67
 	cargo check --verbose --color always --features lightning-transaction-sync
 else
+	# The memchr crate switched to an MSRV of 1.60 starting with v2.6.0
+	# This is currently only a release dependency via core2, which we intend to work with
+	# rust-bitcoin to remove soon.
+	[ "$RUSTC_MINOR_VERSION" -lt 60 ] && cargo update -p memchr --precise "2.5.0" --verbose
 	cargo check --verbose --color always
 fi
+[ "$CI_MINIMIZE_DISK_USAGE" != "" ] && cargo clean
 popd
 
 # Test that we can build downstream code with only the "release pins".
 pushd msrv-no-dev-deps-check
 PIN_RELEASE_DEPS
+# The memchr crate switched to an MSRV of 1.60 starting with v2.6.0
+[ "$RUSTC_MINOR_VERSION" -lt 60 ] && cargo update -p memchr --precise "2.5.0" --verbose
 cargo check
 popd