diff --git a/substrate/client/consensus/babe/src/lib.rs b/substrate/client/consensus/babe/src/lib.rs
index 9bdc08b883..84b018ac59 100644
--- a/substrate/client/consensus/babe/src/lib.rs
+++ b/substrate/client/consensus/babe/src/lib.rs
@@ -466,8 +466,11 @@ impl<B, C, E, I, Error, SO> slots::SimpleSlotWorker<B> for BabeWorker<B, C, E, I
 		head: &B::Header,
 		slot_info: &SlotInfo
 	) -> Option<std::time::Duration> {
-		// never give more than 20 times more lenience.
-		const BACKOFF_CAP: u64 = 20;
+		// never give more than 2^this times the lenience.
+		const BACKOFF_CAP: u64 = 8;
+
+		// how many slots it takes before we double the lenience.
+		const BACKOFF_STEP: u64 = 2;
 
 		let slot_remaining = self.slot_remaining_duration(slot_info);
 		let parent_slot = match find_pre_digest::<B>(head) {
@@ -478,12 +481,22 @@ impl<B, C, E, I, Error, SO> slots::SimpleSlotWorker<B> for BabeWorker<B, C, E, I
 		// we allow a lenience of the number of slots since the head of the
 		// chain was produced, minus 1 (since there is always a difference of at least 1)
 		//
-		// linear back-off.
+		// exponential back-off.
 		// in normal cases we only attempt to issue blocks up to the end of the slot.
 		// when the chain has been stalled for a few slots, we give more lenience.
 		let slot_lenience = slot_info.number.saturating_sub(parent_slot + 1);
+
 		let slot_lenience = std::cmp::min(slot_lenience, BACKOFF_CAP);
-		let slot_lenience = Duration::from_secs(slot_lenience * slot_info.duration);
+		let slot_duration = slot_info.duration << (slot_lenience / BACKOFF_STEP);
+
+		if slot_lenience >= 1 {
+			debug!(target: "babe", "No block for {} slots. Applying 2^({}/{}) lenience",
+				slot_lenience, slot_lenience, BACKOFF_STEP);
+		}
+
+		let slot_duration = slot_info.duration << (slot_lenience / BACKOFF_STEP);
+
+		let slot_lenience = Duration::from_secs(slot_duration);
 		Some(slot_lenience + slot_remaining)
 	}
 }
diff --git a/substrate/frame/support/src/storage/mod.rs b/substrate/frame/support/src/storage/mod.rs
index 1d575d0794..4a392affbd 100644
--- a/substrate/frame/support/src/storage/mod.rs
+++ b/substrate/frame/support/src/storage/mod.rs
@@ -364,8 +364,10 @@ impl<Value: Decode> Iterator for PrefixIterator<Value> {
 	type Item = Value;
 
 	fn next(&mut self) -> Option<Self::Item> {
-		match sp_io::storage::next_key(&self.previous_key) {
-			Some(next_key) if next_key.starts_with(&self.prefix[..]) => {
+		match sp_io::storage::next_key(&self.previous_key)
+			.filter(|n| n.starts_with(&self.prefix[..]))
+		{
+			Some(next_key) => {
 				let value = unhashed::get(&next_key);
 
 				if value.is_none() {