diff --git a/rs/consensus/utils/src/lib.rs b/rs/consensus/utils/src/lib.rs
index cad242cde6f..d05d2c0a049 100644
--- a/rs/consensus/utils/src/lib.rs
+++ b/rs/consensus/utils/src/lib.rs
@@ -171,13 +171,13 @@ pub fn get_adjusted_notary_delay(
         }
         NotaryDelay::ReachedMaxNotarizationCUPGap {
             notarized_height,
-            cup_height,
+            next_cup_height,
         } => {
             warn!(
                 every_n_seconds => 5,
                 log,
                 "The gap between the notarization height ({notarized_height}) and \
-                the CUP height ({cup_height}) exceeds hard bound of \
+                the next CUP height ({next_cup_height}) exceeds hard bound of \
                 {ACCEPTABLE_NOTARIZATION_CUP_GAP}"
             );
             None
@@ -199,7 +199,7 @@ pub enum NotaryDelay {
     /// hard limit on this gap, the notary cannot progress for now.
     ReachedMaxNotarizationCUPGap {
         notarized_height: Height,
-        cup_height: Height,
+        next_cup_height: Height,
     },
 }
 
@@ -257,24 +257,15 @@ pub fn get_adjusted_notary_delay_from_settings(
     let certified_adjusted_delay =
         finality_adjusted_delay + unit_delay.as_millis() as u64 * certified_gap;
 
-    // We measure the gap between our current CUP height and the current notarized
-    // height. If the notarized height is in a DKG interval for which we don't yet have
-    // the CUP, we limit the notarization-CUP gap to ACCEPTABLE_NOTARIZATION_CUP_GAP.
-    let last_cup = pool.get_highest_catch_up_package();
-    let last_cup_dkg_info = &last_cup
-        .content
-        .block
-        .as_ref()
-        .payload
-        .as_ref()
-        .as_summary()
-        .dkg;
-    let cup_height = last_cup.height();
-    let cup_gap = notarized_height.get().saturating_sub(cup_height.get());
-    if cup_gap >= last_cup_dkg_info.interval_length.get() + ACCEPTABLE_NOTARIZATION_CUP_GAP {
+    // We bound the gap between the next CUP height and the current notarization
+    // height by ACCEPTABLE_NOTARIZATION_CUP_GAP.
+    let next_cup_height = pool.get_next_cup_height();
+    if notarized_height.get().saturating_sub(next_cup_height.get())
+        >= ACCEPTABLE_NOTARIZATION_CUP_GAP
+    {
         return NotaryDelay::ReachedMaxNotarizationCUPGap {
             notarized_height,
-            cup_height,
+            next_cup_height,
         };
     }
 
@@ -679,13 +670,13 @@ mod tests {
                 .dkg
                 .clone();
 
-            for _ in 0..last_cup_dkg_info.interval_length.get() {
-                pool.advance_round_normal_operation_no_cup();
-            }
-
-            for _ in 0..(ACCEPTABLE_NOTARIZATION_CUP_GAP - 1) {
-                pool.advance_round_normal_operation_no_cup();
-            }
+            // Advance to next summary height
+            pool.advance_round_normal_operation_no_cup_n(
+                last_cup_dkg_info.interval_length.get() + 1,
+            );
+            assert!(pool.get_cache().finalized_block().payload.is_summary());
+            // Advance to one height before the highest possible CUP-less notarized height
+            pool.advance_round_normal_operation_no_cup_n(ACCEPTABLE_NOTARIZATION_CUP_GAP - 1);
 
             let gap_trigger_height = Height::new(
                 PoolReader::new(&pool).get_notarized_height().get()