diff --git a/RecoTracker/PixelSeeding/plugins/alpaka/CAHitNtuplet.cc b/RecoTracker/PixelSeeding/plugins/alpaka/CAHitNtuplet.cc
index 236e3e53a1825..ff6880e5504b0 100644
--- a/RecoTracker/PixelSeeding/plugins/alpaka/CAHitNtuplet.cc
+++ b/RecoTracker/PixelSeeding/plugins/alpaka/CAHitNtuplet.cc
@@ -15,6 +15,7 @@
 #include "FWCore/Utilities/interface/ESGetToken.h"
 #include "FWCore/Utilities/interface/InputTag.h"
 #include "FWCore/Utilities/interface/RunningAverage.h"
+#include "FWCore/MessageLogger/interface/MessageLogger.h"
 #include "HeterogeneousCore/AlpakaCore/interface/alpaka/EDGetToken.h"
 #include "HeterogeneousCore/AlpakaCore/interface/alpaka/EDPutToken.h"
 #include "HeterogeneousCore/AlpakaCore/interface/alpaka/Event.h"
@@ -358,14 +359,44 @@ namespace ALPAKA_ACCELERATOR_NAMESPACE {
     auto const& geometry = runCache()->get(iEvent.queue());
     auto const& hits = iEvent.get(tokenHit_);
 
-    std::array<double, 1> nHitsV = {{double(hits.nHits())}};
-    std::array<double, 1> emptyV;
-
-    uint32_t const maxTuples = maxNumberOfTuples_.evaluate(nHitsV, emptyV);
-    uint32_t const maxDoublets = maxNumberOfDoublets_.evaluate(nHitsV, emptyV);
+    /// Don't bother if no hits on BPix1 and no good graph for that
+    /// (so no staring pair without BPix1 as first layer).
+    /// TODO: this could be extended to a more general check for
+    /// no hits on any of the starting layers.
+
+    bool hitsOnBPix1 = hits.offsetBPIX2() > 0;
+    bool startNoBPix1 = hitsOnBPix1;  // one would suffice, two for readability
+    if (not hitsOnBPix1) {
+      startNoBPix1 = false;
+      for (const unsigned int& i : globalCache()->startingPairs_) {
+        if (globalCache()->pairGraph_[2 * i] > 0) {
+          startNoBPix1 = true;
+          break;
+        }
+      }
+    }
 
-    iEvent.emplace(tokenTrack_,
-                   deviceAlgo_.makeTuplesAsync(hits, geometry, bf, maxDoublets, maxTuples, iEvent.queue()));
+    if (startNoBPix1) {
+      std::array<double, 1> nHitsV = {{double(hits.nHits())}};
+      std::array<double, 1> emptyV;
+
+      uint32_t const maxTuples = maxNumberOfTuples_.evaluate(nHitsV, emptyV);
+      uint32_t const maxDoublets = maxNumberOfDoublets_.evaluate(nHitsV, emptyV);
+
+      iEvent.emplace(tokenTrack_,
+                     deviceAlgo_.makeTuplesAsync(hits, geometry, bf, maxDoublets, maxTuples, iEvent.queue()));
+
+    } else {
+      edm::LogWarning("CAHitNtupletAlpaka") << "No hit on BPix1 (" << hits.offsetBPIX2()
+                                            << ") and all the starting pairs has BPix1 as inner layer.\nIt's useless "
+                                               "to run the CA. Returning with 0 tracks!";
+      auto& queue = iEvent.queue();
+      const auto device = alpaka::getDev(queue);
+      reco::TracksSoACollection tracks({{0, 0}}, queue);
+      auto ntracks_d = cms::alpakatools::make_device_view(device, tracks.view().nTracks());
+      alpaka::memset(queue, ntracks_d, 0);
+      iEvent.emplace(tokenTrack_, std::move(tracks));
+    }
   }
 
   using CAHitNtupletAlpakaPhase1 = CAHitNtupletAlpaka<pixelTopology::Phase1>;
diff --git a/RecoTracker/PixelSeeding/plugins/alpaka/CAHitNtupletGeneratorKernels.dev.cc b/RecoTracker/PixelSeeding/plugins/alpaka/CAHitNtupletGeneratorKernels.dev.cc
index 65c02aa783f13..3b07ca6ebe1c2 100644
--- a/RecoTracker/PixelSeeding/plugins/alpaka/CAHitNtupletGeneratorKernels.dev.cc
+++ b/RecoTracker/PixelSeeding/plugins/alpaka/CAHitNtupletGeneratorKernels.dev.cc
@@ -57,8 +57,9 @@ namespace ALPAKA_ACCELERATOR_NAMESPACE {
 #ifdef GPU_DEBUG
     std::cout << "Allocation for tuple building with: " << std::endl;
     std::cout << "- nHits          = " << nHits << std::endl;
-    std::cout << "- maxDoublets    = " << maxTuples << std::endl;
-    std::cout << "- maxTracks      = " << maxDoublets << std::endl;
+    std::cout << "- outerHits      = " << outerHits << std::endl;
+    std::cout << "- maxDoublets    = " << maxDoublets << std::endl;
+    std::cout << "- maxTracks      = " << maxTuples << std::endl;
 
     std::cout << "- nCellsToCells  = " << nCellsToCells << std::endl;
     std::cout << "- nHitsToCells   = " << nHitsToCells << std::endl;
diff --git a/RecoTracker/PixelSeeding/plugins/alpaka/CAPixelDoubletsAlgos.h b/RecoTracker/PixelSeeding/plugins/alpaka/CAPixelDoubletsAlgos.h
index 871212e810b64..ef97d1e6f74c7 100644
--- a/RecoTracker/PixelSeeding/plugins/alpaka/CAPixelDoubletsAlgos.h
+++ b/RecoTracker/PixelSeeding/plugins/alpaka/CAPixelDoubletsAlgos.h
@@ -420,9 +420,11 @@ namespace ALPAKA_ACCELERATOR_NAMESPACE::caPixelDoublets {
           }
 
           auto ind = alpaka::atomicAdd(acc, nCells, 1u, alpaka::hierarchy::Blocks{});
-          if (ind >= maxNumOfDoublets) {
+          if (ind >= maxNumOfDoublets or ind >= uint32_t(outerHitHisto->capacity())) {
 #ifdef CA_WARNINGS
-            printf("Warning!!!! Too many cells (limit = %d)!\n", maxNumOfDoublets);
+            printf("Warning!!!! Too many cells (maxNumOfDoublets = %d - nHitsToCell = %d)!\n",
+                   maxNumOfDoublets,
+                   outerHitHisto->capacity());
 #endif
             alpaka::atomicSub(acc, nCells, 1u, alpaka::hierarchy::Blocks{});
             break;