diff --git a/lib/commands/cleanJobsInSet-3.lua b/lib/commands/cleanJobsInSet-3.lua
index 7de75c3a7..98a98d906 100644
--- a/lib/commands/cleanJobsInSet-3.lua
+++ b/lib/commands/cleanJobsInSet-3.lua
@@ -11,52 +11,94 @@
     ARGV[3]  limit the number of jobs to be removed. 0 is unlimited
     ARGV[4]  set name, can be any of 'wait', 'active', 'paused', 'delayed', 'completed', or 'failed'
 ]]
+
+local setKey = KEYS[1]
+local priorityKey = KEYS[2]
+local rateLimiterKey = KEYS[3]
+
+local jobKeyPrefix = ARGV[1]
+local maxTimestamp = ARGV[2]
+local limitStr = ARGV[3]
+local setName = ARGV[4]
+
 local command = "ZRANGE"
 local isList = false
 local rcall = redis.call
 
-if ARGV[4] == "wait" or ARGV[4] == "active" or ARGV[4] == "paused" then
+if setName == "wait" or setName == "active" or setName == "paused" then
   command = "LRANGE"
   isList = true
 end
 
-local jobIds = rcall(command, KEYS[1], 0, -1)
+local limit = tonumber(limitStr)
+local rangeStart = 0
+local rangeEnd = -1
+
+-- If we're only deleting _n_ items, avoid retrieving all items
+-- for faster performance
+--
+-- Start from the tail of the list, since that's where oldest elements
+-- are generally added for FIFO lists
+if limit > 0 then
+  rangeStart = -1 - limit + 1
+  rangeEnd = -1
+end
+
+local jobIds = rcall(command, setKey, rangeStart, rangeEnd)
 local deleted = {}
 local deletedCount = 0
-local limit = tonumber(ARGV[3])
 local jobTS
-for _, jobId in ipairs(jobIds) do
-  if limit > 0 and deletedCount >= limit then
-    break
-  end
 
-  local jobKey = ARGV[1] .. jobId
-  if (rcall("EXISTS", jobKey .. ":lock") == 0) then
-    jobTS = rcall("HGET", jobKey, "timestamp")
-    if (not jobTS or jobTS < ARGV[2]) then
-      if isList then
-        rcall("LREM", KEYS[1], 0, jobId)
-      else
-        rcall("ZREM", KEYS[1], jobId)
-      end
-      rcall("ZREM", KEYS[2], jobId)
-      rcall("DEL", jobKey)
-      rcall("DEL", jobKey .. ":logs")
-
-      -- delete keys related to rate limiter
-      -- NOTE: this code is unncessary for other sets than wait, paused and delayed.
-      local limiterIndexTable = KEYS[3] .. ":index"
-      local limitedSetKey = rcall("HGET", limiterIndexTable, jobId)
-
-      if limitedSetKey then
-        rcall("SREM", limitedSetKey, jobId)
-        rcall("HDEL", limiterIndexTable, jobId)
-      end
+-- Run this loop:
+-- - Once, if limit is -1 or 0
+-- - As many times as needed if limit is positive
+while ((limit <= 0 or deletedCount < limit) and next(jobIds, nil) ~= nil) do
+  for _, jobId in ipairs(jobIds) do
+    if limit > 0 and deletedCount >= limit then
+      break
+    end
+
+    local jobKey = jobKeyPrefix .. jobId
+    if (rcall("EXISTS", jobKey .. ":lock") == 0) then
+      jobTS = rcall("HGET", jobKey, "timestamp")
+      if (not jobTS or jobTS < maxTimestamp) then
+        if isList then
+          rcall("LREM", setKey, 0, jobId)
+        else
+          rcall("ZREM", setKey, jobId)
+        end
+        rcall("ZREM", priorityKey, jobId)
+        rcall("DEL", jobKey)
+        rcall("DEL", jobKey .. ":logs")
+
+        -- delete keys related to rate limiter
+        -- NOTE: this code is unncessary for other sets than wait, paused and delayed.
+        local limiterIndexTable = rateLimiterKey .. ":index"
+        local limitedSetKey = rcall("HGET", limiterIndexTable, jobId)
 
-      deletedCount = deletedCount + 1
-      table.insert(deleted, jobId)
+        if limitedSetKey then
+          rcall("SREM", limitedSetKey, jobId)
+          rcall("HDEL", limiterIndexTable, jobId)
+        end
+
+        deletedCount = deletedCount + 1
+        table.insert(deleted, jobId)
+      end
     end
   end
+
+  -- If we didn't have a limit, return immediately. We should have deleted
+  -- all the jobs we can
+  if limit <= 0 then
+    break
+  end
+
+  if deletedCount < limit then
+    -- We didn't delete enough. Look for more to delete
+    rangeStart = rangeStart - limit
+    rangeEnd = rangeEnd - limit
+    jobIds = rcall(command, setKey, rangeStart, rangeEnd)
+  end
 end
 
 return deleted
diff --git a/test/test_queue.js b/test/test_queue.js
index f211b0f43..e703d600b 100644
--- a/test/test_queue.js
+++ b/test/test_queue.js
@@ -2837,6 +2837,34 @@ describe('Queue', () => {
         });
     });
 
+    it('should clean the number of jobs requested even if first jobs timestamp doesn\'t match', async () => {
+      // This job shouldn't get deleted due to the 5000 grace
+      await queue.add({ some: 'data' });
+      // This job should get cleaned since 10000 > 5000 grace
+      const jobToClean = await queue.add({ some: 'data' }, { timestamp: Date.now() - 10000 });
+      // This job shouldn't get deleted due to the 5000 grace
+      await queue.add({ some: 'data' });
+
+      const cleaned = await queue.clean(5000, 'wait', 1);
+      expect(cleaned.length).to.be.eql(1);
+      expect(cleaned[0]).to.eql(jobToClean.id);
+
+      const len = await queue.count();
+      expect(len).to.be.eql(2);
+    });
+
+    it('shouldn\'t clean anything if all jobs are in grace period', async () => {
+      await queue.add({ some: 'data' });
+      await queue.add({ some: 'data' });
+
+      const cleaned = await queue.clean(5000, 'wait', 1);
+      expect(cleaned.length).to.be.eql(0);
+
+      const cleaned2 = await queue.clean(5000, 'wait');
+      expect(cleaned2.length).to.be.eql(0);
+      expect(await queue.count()).to.be.eql(2);
+    });
+
     it('should properly clean jobs from the priority set', done => {
       const client = new redis(6379, '127.0.0.1', {});
       queue.add({ some: 'data' }, { priority: 5 });