diff --git a/zebra-consensus/src/block.rs b/zebra-consensus/src/block.rs
index 5890cb863..ef18d1b4b 100644
--- a/zebra-consensus/src/block.rs
+++ b/zebra-consensus/src/block.rs
@@ -77,9 +77,24 @@ where
 
         // TODO(jlusby): Error = Report, handle errors from state_service.
         async move {
+            let hash = block.hash();
+
+            // These checks only apply to generated blocks. We check the block
+            // height for parsed blocks when we deserialize them.
+            let height = block
+                .coinbase_height()
+                .ok_or("Invalid block: missing block height.")?;
+            if height > BlockHeight::MAX {
+                Err("Invalid block height: greater than the maximum height.")?;
+            }
+
+            // Check that this block is actually a new block
+            if BlockVerifier::get_block(&mut state, hash).await?.is_some() {
+                Err(format!("Block has already been verified. {:?} {:?}", height, hash))?;
+            }
+
             // Do the difficulty checks first, to raise the threshold for
             // attacks that use any other fields.
-            let hash = block.hash();
             let difficulty_threshold = block.header.difficulty_threshold.to_expanded().ok_or("Invalid difficulty threshold in block header.")?;
             if hash > difficulty_threshold {
                 Err("Block failed the difficulty filter: hash must be less than or equal to the difficulty threshold.")?;
@@ -94,15 +109,6 @@ where
             block.header.is_time_valid_at(now)?;
             block.is_coinbase_first()?;
 
-            // These checks only apply to generated blocks. We check the block
-            // height for parsed blocks when we deserialize them.
-            let height = block
-                .coinbase_height()
-                .ok_or("Invalid block: missing block height.")?;
-            if height > BlockHeight::MAX {
-                Err("Invalid block height: greater than the maximum height.")?;
-            }
-
             // TODO:
             //   - context-free header verification: merkle root
             //   - contextual verification
diff --git a/zebra-consensus/src/chain.rs b/zebra-consensus/src/chain.rs
index 8a15f1be6..65188924f 100644
--- a/zebra-consensus/src/chain.rs
+++ b/zebra-consensus/src/chain.rs
@@ -78,7 +78,6 @@ where
     /// Used for debugging.
     ///
     /// Updated before verification: the block at this height might not be valid.
-    /// Not updated for unexpected high blocks.
     last_block_height: Option<BlockHeight>,
 }
 
@@ -130,10 +129,10 @@ where
             (Some(BlockHeight(block_height)), Some(BlockHeight(last_block_height)))
                 if (block_height > last_block_height + MAX_EXPECTED_BLOCK_GAP) =>
             {
+                self.last_block_height = Some(BlockHeight(block_height));
                 true
             }
             (Some(block_height), _) => {
-                // Update the last height if the block height was expected
                 self.last_block_height = Some(block_height);
                 false
             }
@@ -147,11 +146,15 @@ where
 
             // Call a verifier based on the block height and checkpoints.
             if is_higher_than_max_checkpoint(block_height, max_checkpoint_height) {
-                // Log an info-level message on early high blocks.
+                // Log a message on early high blocks.
                 // The sync service rejects most of these blocks, but we
                 // still want to know if a large number get through.
+                //
+                // This message can also happen if we keep getting unexpected
+                // low blocks. (We can't distinguish between these cases, until
+                // we've verified the blocks.)
                 if is_unexpected_high_block {
-                    tracing::info!(?block_height, "unexpected high block");
+                    tracing::debug!(?block_height, "unexpected high block, or recent unexpected low blocks");
                 }
 
                 block_verifier
diff --git a/zebra-consensus/src/checkpoint.rs b/zebra-consensus/src/checkpoint.rs
index 313f5aff8..8f3ff5aec 100644
--- a/zebra-consensus/src/checkpoint.rs
+++ b/zebra-consensus/src/checkpoint.rs
@@ -330,7 +330,7 @@ impl CheckpointVerifier {
             InitialTip(previous_height) | PreviousCheckpoint(previous_height)
                 if (height <= previous_height) =>
             {
-                Err("block height has already been verified")?
+                Err(format!("Block has already been verified. {:?}", height))?
             }
             InitialTip(_) | PreviousCheckpoint(_) => {}
             // We're finished, so no checkpoint height is valid
@@ -394,7 +394,9 @@ impl CheckpointVerifier {
         let height = match self.check_block(&block) {
             Ok(height) => height,
             Err(error) => {
-                tracing::warn!(?error);
+                // Block errors happen frequently on mainnet, due to bad peers.
+                tracing::debug!(?error);
+
                 // Sending might fail, depending on what the caller does with rx,
                 // but there's nothing we can do about it.
                 let _ = tx.send(Err(error));
@@ -573,7 +575,7 @@ impl CheckpointVerifier {
             } else {
                 // The last block height we processed did not have any blocks
                 // with a matching hash, so chain verification has failed.
-                tracing::warn!(
+                tracing::info!(
                     ?current_height,
                     ?current_range,
                     "No valid blocks at height in CheckpointVerifier"