diff --git a/ci/ci-tests.sh b/ci/ci-tests.sh
index 8c675a654be..7b925cc8544 100755
--- a/ci/ci-tests.sh
+++ b/ci/ci-tests.sh
@@ -29,6 +29,9 @@ 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
+[ "$RUSTC_MINOR_VERSION" -lt 56 ] && cargo update -p syn:2.0.33 --precise "2.0.32" --verbose
+
 # The proc-macro2 crate switched to Rust edition 2021 starting with v1.0.66, i.e., has MSRV of 1.56
 [ "$RUSTC_MINOR_VERSION" -lt 56 ] && cargo update -p proc-macro2 --precise "1.0.65" --verbose
 
@@ -120,6 +123,10 @@ 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
 popd
diff --git a/lightning-transaction-sync/tests/integration_tests.rs b/lightning-transaction-sync/tests/integration_tests.rs
index 151f986553f..617b1213e89 100644
--- a/lightning-transaction-sync/tests/integration_tests.rs
+++ b/lightning-transaction-sync/tests/integration_tests.rs
@@ -321,20 +321,3 @@ async fn test_esplora_syncs() {
 		_ => panic!("Unexpected event"),
 	}
 }
-
-#[tokio::test]
-#[cfg(any(feature = "esplora-async-https", feature = "esplora-blocking"))]
-async fn test_esplora_connects_to_public_server() {
-	let mut logger = TestLogger {};
-	let esplora_url = "https://blockstream.info/api".to_string();
-	let tx_sync = EsploraSyncClient::new(esplora_url, &mut logger);
-	let confirmable = TestConfirmable::new();
-
-	// Check we connect and pick up on new best blocks
-	assert_eq!(confirmable.best_block.lock().unwrap().1, 0);
-	#[cfg(feature = "esplora-async-https")]
-	tx_sync.sync(vec![&confirmable]).await.unwrap();
-	#[cfg(feature = "esplora-blocking")]
-	tx_sync.sync(vec![&confirmable]).unwrap();
-	assert_ne!(confirmable.best_block.lock().unwrap().1, 0);
-}