diff --git a/src/commands/cleanJobsInSet-2.lua b/src/commands/cleanJobsInSet-2.lua
index 20f06b9352..c33c64eb11 100644
--- a/src/commands/cleanJobsInSet-2.lua
+++ b/src/commands/cleanJobsInSet-2.lua
@@ -34,13 +34,19 @@ local result
 if ARGV[4] == "active" then
   result = cleanList(KEYS[1], ARGV[1], rangeStart, rangeEnd, ARGV[2], false)
 elseif ARGV[4] == "delayed" then
-  result = cleanSet(KEYS[1], ARGV[1], rangeStart, rangeEnd, ARGV[2], limit, {"processedOn", "timestamp"})
+  rangeEnd = "+inf"
+  result = cleanSet(KEYS[1], ARGV[1], rangeEnd, ARGV[2], limit,
+                    {"processedOn", "timestamp"}, false)
 elseif ARGV[4] == "prioritized" then
-  result = cleanSet(KEYS[1], ARGV[1], rangeStart, rangeEnd, ARGV[2], limit, {"timestamp"})
+  rangeEnd = "+inf"
+  result = cleanSet(KEYS[1], ARGV[1], rangeEnd, ARGV[2], limit,
+                    {"timestamp"}, false)
 elseif ARGV[4] == "wait" or ARGV[4] == "paused" then
   result = cleanList(KEYS[1], ARGV[1], rangeStart, rangeEnd, ARGV[2], true)
 else
-  result = cleanSet(KEYS[1], ARGV[1], rangeStart, rangeEnd, ARGV[2], limit, {"finishedOn"} )
+  rangeEnd = ARGV[2]
+  result = cleanSet(KEYS[1], ARGV[1], rangeEnd, ARGV[2], limit,
+                    {"finishedOn"}, true)
 end
 
 rcall("XADD", KEYS[2], "*", "event", "cleaned", "count", result[2])
diff --git a/src/commands/includes/cleanList.lua b/src/commands/includes/cleanList.lua
index f7e7a65225..99b397ef53 100644
--- a/src/commands/includes/cleanList.lua
+++ b/src/commands/includes/cleanList.lua
@@ -30,7 +30,7 @@ local function cleanList(listKey, jobKeyPrefix, rangeStart, rangeEnd,
       -- Fetch all three of these (in that order) and use the first one that is set so that we'll leave jobs
       -- that have been active within the grace period:
       jobTS = getTimestamp(jobKey, {"finishedOn", "processedOn", "timestamp"})
-      if (not jobTS or jobTS < timestamp) then
+      if (not jobTS or jobTS <= timestamp) then
         -- replace the entry with a deletion marker; the actual deletion will
         -- occur at the end of the script
         rcall("LSET", listKey, rangeEnd - jobIdsLen + i, deletionMarker)
diff --git a/src/commands/includes/cleanSet.lua b/src/commands/includes/cleanSet.lua
index 3f795ccdd6..f83393d50a 100644
--- a/src/commands/includes/cleanSet.lua
+++ b/src/commands/includes/cleanSet.lua
@@ -9,8 +9,8 @@
 --- @include "getTimestamp"
 --- @include "removeJob"
 
-local function cleanSet(setKey, jobKeyPrefix, rangeStart, rangeEnd, timestamp, limit, attributes)
-  local jobs = getJobsInZset(setKey, rangeStart, rangeEnd, timestamp, limit)
+local function cleanSet(setKey, jobKeyPrefix, rangeEnd, timestamp, limit, attributes, isFinished)
+  local jobs = getJobsInZset(setKey, rangeEnd, limit)
   local deleted = {}
   local deletedCount = 0
   local jobTS
@@ -20,12 +20,18 @@ local function cleanSet(setKey, jobKeyPrefix, rangeStart, rangeEnd, timestamp, l
     end
 
     local jobKey = jobKeyPrefix .. job
-    -- * finishedOn says when the job was completed, but it isn't set unless the job has actually completed
-    jobTS = getTimestamp(jobKey, attributes)
-    if (not jobTS or jobTS < timestamp) then
+    if isFinished then
       removeJob(job, true, jobKeyPrefix)
       deletedCount = deletedCount + 1
       table.insert(deleted, job)
+    else
+      -- * finishedOn says when the job was completed, but it isn't set unless the job has actually completed
+      jobTS = getTimestamp(jobKey, attributes)
+      if (not jobTS or jobTS <= timestamp) then
+        removeJob(job, true, jobKeyPrefix)
+        deletedCount = deletedCount + 1
+        table.insert(deleted, job)
+      end
     end
   end
 
diff --git a/src/commands/includes/getJobsInZset.lua b/src/commands/includes/getJobsInZset.lua
index f2f4ab1f37..a9f90c3960 100644
--- a/src/commands/includes/getJobsInZset.lua
+++ b/src/commands/includes/getJobsInZset.lua
@@ -2,11 +2,10 @@
 -- of items in a sorted set only run a single iteration. If we simply used
 -- ZRANGE, we may take a long time traversing through jobs that are within the
 -- grace period.
-local function getJobsInZset(zsetKey, rangeStart, rangeEnd, maxTimestamp, limit)
+local function getJobsInZset(zsetKey, rangeEnd, limit)
   if limit > 0 then
-    return rcall("ZRANGEBYSCORE", zsetKey, 0, maxTimestamp, "LIMIT", 0, limit)
+    return rcall("ZRANGEBYSCORE", zsetKey, 0, rangeEnd, "LIMIT", 0, limit)
   else
-    return rcall("ZRANGE", zsetKey, rangeStart, rangeEnd)
+    return rcall("ZRANGEBYSCORE", zsetKey, 0, rangeEnd)
   end
 end
-  
\ No newline at end of file
diff --git a/tests/test_clean.ts b/tests/test_clean.ts
index 5415083f30..5106178f3a 100644
--- a/tests/test_clean.ts
+++ b/tests/test_clean.ts
@@ -175,6 +175,26 @@ describe('Cleaner', () => {
     expect(count).to.be.eql(0);
   });
 
+  it('should clean all delayed jobs when limit is given', async () => {
+    await queue.add('test', { some: 'data' }, { delay: 5000 });
+    await queue.add('test', { some: 'data' }, { delay: 5000 });
+    await delay(100);
+    const jobs = await queue.clean(0, 1000, 'delayed');
+    expect(jobs.length).to.be.eql(2);
+    const count = await queue.count();
+    expect(count).to.be.eql(0);
+  });
+
+  it('should clean all prioritized jobs when limit is given', async () => {
+    await queue.add('test', { some: 'data' }, { priority: 5000 });
+    await queue.add('test', { some: 'data' }, { priority: 5001 });
+    await delay(100);
+    const jobs = await queue.clean(0, 1000, 'prioritized');
+    expect(jobs.length).to.be.eql(2);
+    const count = await queue.count();
+    expect(count).to.be.eql(0);
+  });
+
   describe('when prioritized state is provided', async () => {
     it('should clean the number of jobs requested', async () => {
       await queue.add('test', { some: 'data' }, { priority: 1 }); // as queue is empty, this job will be added to wait