diff --git a/zebra-consensus/src/checkpoint.rs b/zebra-consensus/src/checkpoint.rs
index 99120912..bcb93a98 100644
--- a/zebra-consensus/src/checkpoint.rs
+++ b/zebra-consensus/src/checkpoint.rs
@@ -79,7 +79,14 @@ pub const MAX_QUEUED_BLOCKS_PER_HEIGHT: usize = 4;
 
 /// We limit the maximum number of blocks in each checkpoint. Each block uses a
 /// constant amount of memory for the supporting data structures and futures.
-pub const MAX_CHECKPOINT_HEIGHT_GAP: usize = 2_000;
+///
+/// We choose a checkpoint gap that allows us to verify one checkpoint for
+/// every `ObtainTips` or `ExtendTips` response.
+///
+/// `zcashd`'s maximum `FindBlocks` response size is 500 hashes. `zebrad` uses
+/// 1 hash to verify the tip, and discards 1-2 hashes to work around `zcashd`
+/// bugs. So the most efficient gap is slightly less than 500 blocks.
+pub const MAX_CHECKPOINT_HEIGHT_GAP: usize = 400;
 
 /// A checkpointing block verifier.
 ///
diff --git a/zebra-utils/src/bin/zebra-checkpoints/main.rs b/zebra-utils/src/bin/zebra-checkpoints/main.rs
index 90ba5e17..406a3619 100644
--- a/zebra-utils/src/bin/zebra-checkpoints/main.rs
+++ b/zebra-utils/src/bin/zebra-checkpoints/main.rs
@@ -25,10 +25,10 @@ use std::os::unix::process::ExitStatusExt;
 mod args;
 
 /// We limit the memory usage for each checkpoint, based on the cumulative size of
-/// the serialized blocks in the chain. Deserialized blocks are larger, because
-/// they contain pointers and non-compact integers. But they should be within a
-/// constant factor of the serialized size.
-const MAX_CHECKPOINT_BYTE_COUNT: u64 = 256 * 1024 * 1024;
+/// the serialized blocks in the chain. Deserialized blocks are slightly larger
+/// than serialized blocks, but they should be within a constant factor of the
+/// serialized size.
+const MAX_CHECKPOINT_BYTE_COUNT: u64 = 32 * 1024 * 1024;
 
 /// Initialise tracing using its defaults.
 fn init_tracing() {