diff --git a/lightning/src/ln/offers_tests.rs b/lightning/src/ln/offers_tests.rs
index 54dc5e4a598..e16c0ed515f 100644
--- a/lightning/src/ln/offers_tests.rs
+++ b/lightning/src/ln/offers_tests.rs
@@ -250,7 +250,7 @@ fn prefers_non_tor_nodes_in_blinded_paths() {
 	disconnect_peers(david, &[bob, &nodes[4], &nodes[5]]);
 
 	let tor = SocketAddress::OnionV2([255, 254, 253, 252, 251, 250, 249, 248, 247, 246, 38, 7]);
-	announce_node_address(charlie, &[alice, bob, david, &nodes[4], &nodes[5]], tor);
+	announce_node_address(charlie, &[alice, bob, david, &nodes[4], &nodes[5]], tor.clone());
 
 	let offer = bob.node
 		.create_offer_builder("coffee".to_string()).unwrap()
@@ -259,8 +259,73 @@ fn prefers_non_tor_nodes_in_blinded_paths() {
 	assert_ne!(offer.signing_pubkey(), bob_id);
 	assert!(!offer.paths().is_empty());
 	for path in offer.paths() {
+		assert_ne!(path.introduction_node_id, bob_id);
 		assert_ne!(path.introduction_node_id, charlie_id);
 	}
+
+	// Use a one-hop blinded path when Bob is announced and all his peers are Tor-only.
+	announce_node_address(&nodes[4], &[alice, bob, charlie, david, &nodes[5]], tor.clone());
+	announce_node_address(&nodes[5], &[alice, bob, charlie, david, &nodes[4]], tor.clone());
+
+	let offer = bob.node
+		.create_offer_builder("coffee".to_string()).unwrap()
+		.amount_msats(10_000_000)
+		.build().unwrap();
+	assert_ne!(offer.signing_pubkey(), bob_id);
+	assert!(!offer.paths().is_empty());
+	for path in offer.paths() {
+		assert_eq!(path.introduction_node_id, bob_id);
+	}
+}
+
+/// Checks that blinded paths prefer an introduction node that is the most connected.
+#[test]
+fn prefers_more_connected_nodes_in_blinded_paths() {
+	let mut accept_forward_cfg = test_default_channel_config();
+	accept_forward_cfg.accept_forwards_to_priv_channels = true;
+
+	let mut features = channelmanager::provided_init_features(&accept_forward_cfg);
+	features.set_onion_messages_optional();
+	features.set_route_blinding_optional();
+
+	let chanmon_cfgs = create_chanmon_cfgs(6);
+	let node_cfgs = create_node_cfgs(6, &chanmon_cfgs);
+
+	*node_cfgs[1].override_init_features.borrow_mut() = Some(features);
+
+	let node_chanmgrs = create_node_chanmgrs(
+		6, &node_cfgs, &[None, Some(accept_forward_cfg), None, None, None, None]
+	);
+	let nodes = create_network(6, &node_cfgs, &node_chanmgrs);
+
+	create_unannounced_chan_between_nodes_with_value(&nodes, 0, 1, 10_000_000, 1_000_000_000);
+	create_unannounced_chan_between_nodes_with_value(&nodes, 2, 3, 10_000_000, 1_000_000_000);
+	create_announced_chan_between_nodes_with_value(&nodes, 1, 2, 10_000_000, 1_000_000_000);
+	create_announced_chan_between_nodes_with_value(&nodes, 1, 4, 10_000_000, 1_000_000_000);
+	create_announced_chan_between_nodes_with_value(&nodes, 1, 5, 10_000_000, 1_000_000_000);
+	create_announced_chan_between_nodes_with_value(&nodes, 2, 4, 10_000_000, 1_000_000_000);
+	create_announced_chan_between_nodes_with_value(&nodes, 2, 5, 10_000_000, 1_000_000_000);
+
+	// Add extra channels so that more than one of Bob's peers have MIN_PEER_CHANNELS and one has
+	// more than the others.
+	create_announced_chan_between_nodes_with_value(&nodes, 0, 4, 10_000_000, 1_000_000_000);
+	create_announced_chan_between_nodes_with_value(&nodes, 3, 4, 10_000_000, 1_000_000_000);
+
+	let (alice, bob, charlie, david) = (&nodes[0], &nodes[1], &nodes[2], &nodes[3]);
+	let bob_id = bob.node.get_our_node_id();
+
+	disconnect_peers(alice, &[charlie, david, &nodes[4], &nodes[5]]);
+	disconnect_peers(david, &[bob, &nodes[4], &nodes[5]]);
+
+	let offer = bob.node
+		.create_offer_builder("coffee".to_string()).unwrap()
+		.amount_msats(10_000_000)
+		.build().unwrap();
+	assert_ne!(offer.signing_pubkey(), bob_id);
+	assert!(!offer.paths().is_empty());
+	for path in offer.paths() {
+		assert_eq!(path.introduction_node_id, nodes[4].node.get_our_node_id());
+	}
 }
 
 /// Checks that an offer can be paid through blinded paths and that ephemeral pubkeys are used
diff --git a/lightning/src/onion_message/messenger.rs b/lightning/src/onion_message/messenger.rs
index c221e782025..37de5504532 100644
--- a/lightning/src/onion_message/messenger.rs
+++ b/lightning/src/onion_message/messenger.rs
@@ -358,19 +358,28 @@ where
 		const MIN_PEER_CHANNELS: usize = 3;
 
 		let network_graph = self.network_graph.deref().read_only();
+		let is_recipient_announced =
+			network_graph.nodes().contains_key(&NodeId::from_pubkey(&recipient));
+
 		let mut peer_info = peers.iter()
 			// Limit to peers with announced channels
 			.filter_map(|pubkey|
 				network_graph
 					.node(&NodeId::from_pubkey(pubkey))
 					.filter(|info| info.channels.len() >= MIN_PEER_CHANNELS)
-					.map(|info| (*pubkey, info.is_tor_only()))
+					.map(|info| (*pubkey, info.is_tor_only(), info.channels.len()))
 			)
+			// Exclude Tor-only nodes when the recipient is announced.
+			.filter(|(_, is_tor_only, _)| !(*is_tor_only && is_recipient_announced))
 			.collect::<Vec<_>>();
-		peer_info.sort_unstable_by(|(_, a_tor_only), (_, b_tor_only)| a_tor_only.cmp(b_tor_only));
+
+		// Prefer using non-Tor nodes with the most channels as the introduction node.
+		peer_info.sort_unstable_by(|(_, a_tor_only, a_channels), (_, b_tor_only, b_channels)| {
+			a_tor_only.cmp(b_tor_only).then(a_channels.cmp(b_channels).reverse())
+		});
 
 		let paths = peer_info.into_iter()
-			.map(|(pubkey, _)| vec![pubkey, recipient])
+			.map(|(pubkey, _, _)| vec![pubkey, recipient])
 			.map(|node_pks| BlindedPath::new_for_message(&node_pks, &*self.entropy_source, secp_ctx))
 			.take(MAX_PATHS)
 			.collect::<Result<Vec<_>, _>>();
@@ -378,7 +387,7 @@ where
 		match paths {
 			Ok(paths) if !paths.is_empty() => Ok(paths),
 			_ => {
-				if network_graph.nodes().contains_key(&NodeId::from_pubkey(&recipient)) {
+				if is_recipient_announced {
 					BlindedPath::one_hop_for_message(recipient, &*self.entropy_source, secp_ctx)
 						.map(|path| vec![path])
 				} else {