diff --git a/FWCore/Framework/interface/EventProcessor.h b/FWCore/Framework/interface/EventProcessor.h
index 7740f0afbd2b2..c7cf9b2ed83f7 100644
--- a/FWCore/Framework/interface/EventProcessor.h
+++ b/FWCore/Framework/interface/EventProcessor.h
@@ -241,6 +241,8 @@ namespace edm {
 
     bool shouldWeStop() const;
 
+    void tryToMakeOtherStreamsSkipLumi(unsigned int iStreamIndex, LuminosityBlockProcessingStatus& iStatus);
+
     void setExceptionMessageFiles(std::string& message);
     void setExceptionMessageRuns();
     void setExceptionMessageLumis();
diff --git a/FWCore/Framework/src/EventProcessor.cc b/FWCore/Framework/src/EventProcessor.cc
index 76de43cb7a500..ccaccb12efd87 100644
--- a/FWCore/Framework/src/EventProcessor.cc
+++ b/FWCore/Framework/src/EventProcessor.cc
@@ -1732,6 +1732,9 @@ namespace edm {
                             streamQueuesInserter_.push(*holder.group(), [this, status, holder, &es]() mutable {
                               for (unsigned int i = 0; i < preallocations_.numberOfStreams(); ++i) {
                                 streamQueues_[i].push(*holder.group(), [this, i, status, holder, &es]() mutable {
+                                  if (!status->setStreamStartedLumi(i)) {
+                                    return;
+                                  }
                                   streamQueues_[i].pause();
 
                                   auto& event = principalCache_.eventPrincipal(i);
@@ -2256,6 +2259,7 @@ namespace edm {
                 // If appropriate, this will also start the next run.
                 endRunAsync(streamRunStatus_[iStreamIndex], iTask);
               }
+              tryToMakeOtherStreamsSkipLumi(iStreamIndex, *status);
             }
             streamEndLumiAsync(iTask, iStreamIndex);
           } else {
@@ -2386,6 +2390,19 @@ namespace edm {
     return schedule_->terminate();
   }
 
+  void EventProcessor::tryToMakeOtherStreamsSkipLumi(unsigned int iStreamIndex,
+                                                     LuminosityBlockProcessingStatus& iStatus) {
+    for (unsigned int stream = 0; stream < preallocations_.numberOfStreams(); ++stream) {
+      if (stream == iStreamIndex) {
+        continue;
+      }
+      if (iStatus.setStreamStartedLumi(stream)) {
+        // This cannot be the last stream to end the lumi, but we must decrement the counter
+        iStatus.streamFinishedLumi();
+      }
+    }
+  }
+
   void EventProcessor::setExceptionMessageFiles(std::string& message) { exceptionMessageFiles_ = message; }
 
   void EventProcessor::setExceptionMessageRuns() { exceptionMessageRuns_ = true; }
diff --git a/FWCore/Framework/src/LuminosityBlockProcessingStatus.cc b/FWCore/Framework/src/LuminosityBlockProcessingStatus.cc
index 1b77c83f35e88..a808bfa7757b9 100644
--- a/FWCore/Framework/src/LuminosityBlockProcessingStatus.cc
+++ b/FWCore/Framework/src/LuminosityBlockProcessingStatus.cc
@@ -14,6 +14,14 @@
 #include "FWCore/Framework/interface/LuminosityBlockPrincipal.h"
 
 namespace edm {
+
+  LuminosityBlockProcessingStatus::LuminosityBlockProcessingStatus(unsigned int iNStreams)
+      : streamStartedLumi_(iNStreams), nStreamsStillProcessingLumi_(iNStreams) {
+    for (auto& item : streamStartedLumi_) {
+      item.store(false);
+    }
+  }
+
   void LuminosityBlockProcessingStatus::resetResources() {
     endIOVWaitingTasks_.doneWaiting(std::exception_ptr{});
     for (auto& iter : eventSetupImpls_) {
@@ -26,6 +34,11 @@ namespace edm {
     globalEndRunHolder_ = std::move(holder);
   }
 
+  bool LuminosityBlockProcessingStatus::setStreamStartedLumi(unsigned int iStream) {
+    bool expected = false;
+    return streamStartedLumi_.at(iStream).compare_exchange_strong(expected, true);
+  }
+
   void LuminosityBlockProcessingStatus::setEndTime() {
     constexpr char kUnset = 0;
     constexpr char kSetting = 1;
diff --git a/FWCore/Framework/src/LuminosityBlockProcessingStatus.h b/FWCore/Framework/src/LuminosityBlockProcessingStatus.h
index b35b4c5258049..ad0f030bdd1bc 100644
--- a/FWCore/Framework/src/LuminosityBlockProcessingStatus.h
+++ b/FWCore/Framework/src/LuminosityBlockProcessingStatus.h
@@ -39,7 +39,7 @@ namespace edm {
 
   class LuminosityBlockProcessingStatus {
   public:
-    LuminosityBlockProcessingStatus(unsigned int iNStreams) : nStreamsStillProcessingLumi_(iNStreams) {}
+    LuminosityBlockProcessingStatus(unsigned int iNStreams);
 
     LuminosityBlockProcessingStatus(LuminosityBlockProcessingStatus const&) = delete;
     LuminosityBlockProcessingStatus const& operator=(LuminosityBlockProcessingStatus const&) = delete;
@@ -70,6 +70,8 @@ namespace edm {
     void setGlobalEndRunHolder(WaitingTaskHolder);
     void globalEndRunHolderDoneWaiting() { globalEndRunHolder_.doneWaiting(std::exception_ptr{}); }
 
+    bool setStreamStartedLumi(unsigned int iStream);
+
     bool streamFinishedLumi() { return 0 == (--nStreamsStillProcessingLumi_); }
 
     //These should only be called while in the InputSource's task queue
@@ -103,6 +105,7 @@ namespace edm {
     std::vector<std::shared_ptr<const EventSetupImpl>> eventSetupImpls_;
     WaitingTaskList endIOVWaitingTasks_;
     edm::WaitingTaskHolder globalEndRunHolder_;
+    std::vector<std::atomic<bool>> streamStartedLumi_;
     std::atomic<unsigned int> nStreamsStillProcessingLumi_{0};  //read/write as streams finish lumi so must be atomic
     edm::Timestamp endTime_{};
     std::atomic<char> endTimeSetStatus_{0};