diff --git a/zebrad/src/components/inbound/downloads.rs b/zebrad/src/components/inbound/downloads.rs
index d138a1e99..97192d28b 100644
--- a/zebrad/src/components/inbound/downloads.rs
+++ b/zebrad/src/components/inbound/downloads.rs
@@ -21,6 +21,30 @@ use zebra_state as zs;
 
 type BoxError = Box<dyn std::error::Error + Send + Sync + 'static>;
 
+/// The maximum number of concurrent inbound download and verify tasks.
+///
+/// Set to one and a half checkpoint intervals, so that the inbound queue can
+/// hold a complete checkpoint interval, if needed. We expect the syncer to
+/// download and verify checkpoints, so this bound might never be reached.
+const MAX_INBOUND_CONCURRENCY: usize = zebra_consensus::MAX_CHECKPOINT_HEIGHT_GAP * 3 / 2;
+
+/// The action taken in response to a peer's gossipped block hash.
+pub enum DownloadAction {
+    /// The block hash was successfully queued for download and verification.
+    AddedToQueue,
+
+    /// The block hash is already queued, so this request was ignored.
+    ///
+    /// Another peer has already gossipped the same hash to us.
+    AlreadyQueued,
+
+    /// The queue is at capacity, so this request was ignored.
+    ///
+    /// The sync service should discover this block later, when we are closer
+    /// to the tip. The queue's capacity is [`MAX_INBOUND_CONCURRENCY`].
+    FullQueue,
+}
+
 /// Manages download and verification of blocks gossiped to this peer.
 #[pin_project]
 #[derive(Debug)]
@@ -116,12 +140,27 @@ where
 
     /// Queue a block for download and verification.
     ///
-    /// Returns true if the block was newly queued, and false if it was already queued.
+    /// Returns the action taken in response to the queue request.
     #[instrument(skip(self, hash), fields(hash = %hash))]
-    pub fn download_and_verify(&mut self, hash: block::Hash) -> bool {
+    pub fn download_and_verify(&mut self, hash: block::Hash) -> DownloadAction {
         if self.cancel_handles.contains_key(&hash) {
-            tracing::debug!("hash already queued for download");
-            return false;
+            tracing::debug!(
+                ?hash,
+                queue_len = self.pending.len(),
+                ?MAX_INBOUND_CONCURRENCY,
+                "block hash already queued for inbound download: ignored block"
+            );
+            return DownloadAction::AlreadyQueued;
+        }
+
+        if self.pending.len() >= MAX_INBOUND_CONCURRENCY {
+            tracing::info!(
+                ?hash,
+                queue_len = self.pending.len(),
+                ?MAX_INBOUND_CONCURRENCY,
+                "too many blocks queued for inbound download: ignored block"
+            );
+            return DownloadAction::FullQueue;
         }
 
         // This oneshot is used to signal cancellation to the download task.
@@ -182,7 +221,14 @@ where
             "blocks are only queued once"
         );
 
-        tracing::debug!("queued hash for download");
-        true
+        tracing::debug!(
+            ?hash,
+            queue_len = self.pending.len(),
+            ?MAX_INBOUND_CONCURRENCY,
+            "queued hash for download"
+        );
+        metrics::gauge!("gossip.queued.block.count", self.pending.len() as _);
+
+        DownloadAction::AddedToQueue
     }
 }