diff --git a/hist/hist/src/THnBase.cxx b/hist/hist/src/THnBase.cxx
index 556808364863b..ebed694679f14 100644
--- a/hist/hist/src/THnBase.cxx
+++ b/hist/hist/src/THnBase.cxx
@@ -836,10 +836,14 @@ void THnBase::AddInternal(const THnBase* h, Double_t c, Bool_t rebinned)
    Long64_t i = 0;
    std::unique_ptr<ROOT::Internal::THnBaseBinIter> iter{h->CreateIter(false)};
    // Add to this whatever is found inside the other histogram
+   const bool sparse = InheritsFrom(THnSparse::Class());
    while ((i = iter->Next(coord)) >= 0) {
       // Get the content of the bin from the second histogram
       Double_t v = h->GetBinContent(i);
-
+      Double_t err2 = haveErrors ? h->GetBinError2(i) * c * c : 0;
+      if (sparse && v == 0 && err2 == 0) {
+         continue;
+      }
       Long64_t mybinidx = -1;
       if (rebinned) {
          // Get the bin center given a coord
@@ -852,7 +856,6 @@ void THnBase::AddInternal(const THnBase* h, Double_t c, Bool_t rebinned)
       }
 
       if (haveErrors) {
-         Double_t err2 = h->GetBinError2(i) * c * c;
          AddBinError2(mybinidx, err2);
       }
       // only _after_ error calculation, or sqrt(v) is taken into account!
diff --git a/hist/hist/test/THn.cxx b/hist/hist/test/THn.cxx
index e7dd8aae022c2..c9a682acb1123 100644
--- a/hist/hist/test/THn.cxx
+++ b/hist/hist/test/THn.cxx
@@ -1,6 +1,7 @@
 #include "gtest/gtest.h"
 
 #include "THn.h"
+#include "THnSparse.h"
 #include "TH1.h"
 #include "TH2.h"
 
@@ -174,3 +175,16 @@ TEST(THn, ErrorsOfProjection)
    EXPECT_FLOAT_EQ(proj->GetBinContent(projectedBin2), 18.);
    EXPECT_FLOAT_EQ(proj->GetBinError(projectedBin2), 6.);
 }
+
+// https://github.com/root-project/root/issues/19366
+TEST(THn, CreateSparse)
+{
+   Int_t bins[1] = {5};
+   Double_t xmin[1] = {0.};
+   Double_t xmax[1] = {1.};
+   THnD hn("hn", "hn", 1, bins, xmin, xmax);
+   hn.Fill(0.5);
+   auto hn_sparse = THnSparseD::CreateSparse("", "", &hn);
+   EXPECT_EQ(hn_sparse->GetNbins(), 1);
+   EXPECT_FLOAT_EQ(hn_sparse->GetSparseFractionBins(), 1. / 7); // 5 + under/overflows
+}