diff --git a/hist/hist/src/THLimitsFinder.cxx b/hist/hist/src/THLimitsFinder.cxx
index 528b08303f651..fe0533b02db3e 100644
--- a/hist/hist/src/THLimitsFinder.cxx
+++ b/hist/hist/src/THLimitsFinder.cxx
@@ -12,6 +12,8 @@
 #include "TMath.h"
 #include "THLimitsFinder.h"
 
+#include <algorithm>
+
 THLimitsFinder *THLimitsFinder::fgLimitsFinder = nullptr;
 
 ClassImp(THLimitsFinder);
@@ -381,8 +383,8 @@ void THLimitsFinder::OptimizeLimits(Int_t nbins, Int_t &newbins, Double_t &xmin,
       xmin = -1;
       xmax = 1;
    } else {
-      xmin    = binlow;
-      xmax    = binhigh;
+      xmin = std::min(binlow, xmin);
+      xmax = std::max(binhigh, xmax + 0.01 * (xmax - xmin));
    }
    if (isInteger) {
       Long64_t ixmin = Long64_t(xmin);
diff --git a/hist/hist/test/test_TH1.cxx b/hist/hist/test/test_TH1.cxx
index 6b625eb7ae528..381d04050f430 100644
--- a/hist/hist/test/test_TH1.cxx
+++ b/hist/hist/test/test_TH1.cxx
@@ -54,6 +54,19 @@ TEST(THLimitsFinder, Degenerate)
    EXPECT_GE(xmax, centralValue + 5.);
 }
 
+// see https://root-forum.cern.ch/t/bug-or-feature-in-ttree-draw/62862
+// Due to a poor binning choice in THLimitsFinder, the histograms in
+// TTree::Draw might not contain contain all values.
+TEST(THLimitsFinder, TTreeDraw_AutoBinning)
+{
+   TH1F histo("limitsFinder", "", 100, 0, 0);
+   histo.Fill(-999);
+   histo.Fill(0);
+   histo.BufferEmpty(1);
+
+   EXPECT_EQ(histo.GetEntries(), histo.GetEffectiveEntries());
+}
+
 // Simple cross-check that TH1::SmoothArray() is not doing anything if input
 // array is already smooth.
 TEST(TH1, SmoothArrayCrossCheck)
diff --git a/test/stressHistogram.cxx b/test/stressHistogram.cxx
index 8e153d92209d9..09b3e64750c6a 100644
--- a/test/stressHistogram.cxx
+++ b/test/stressHistogram.cxx
@@ -6282,6 +6282,9 @@ bool testMerge1DWithBuffer(bool allNoLimits)
    TH1D* h4 = new TH1D("h4", "h4-Title", numberOfBins, x1,x2);
 
    h0->Sumw2(); h1->Sumw2();h2->Sumw2();h4->Sumw2();
+   // The below histograms will be merged into h0, so they all need to fit into the buffer.
+   // Otherwise, the axis ranges will be computed already during the partial merge.
+   h0->SetBuffer(nEvents * 10);
    h1->SetBuffer(nEvents*10);
    h2->SetBuffer(nEvents*10);
    h3->SetBuffer(nEvents*10);
diff --git a/tree/tree/test/TTreeRegressions.cxx b/tree/tree/test/TTreeRegressions.cxx
index 06db04154e6d0..d73b9641f4fe1 100644
--- a/tree/tree/test/TTreeRegressions.cxx
+++ b/tree/tree/test/TTreeRegressions.cxx
@@ -289,3 +289,23 @@ TEST(TTreeRegressions, FindBranchBrackets)
    EXPECT_NE(t.FindBranch("branch[3]"), nullptr);
    EXPECT_EQ(t.FindBranch("branch[3]"), t.GetBranch("branch[3]"));
 }
+
+// see https://root-forum.cern.ch/t/bug-or-feature-in-ttree-draw/62862
+// Due to a poor binning choice in THLimitsFinder, the histogram didn't contain
+// all values.
+TEST(TTreeRegressions, DrawAutoBinning)
+{
+   TTree t;
+   Float_t x;
+   t.Branch("x", &x);
+   x = -999;
+   t.Fill();
+   x = 0;
+   t.Fill();
+   t.Draw("x");
+   auto h = (TH1 *)gROOT->FindObject("htemp");
+   ASSERT_NE(h, nullptr);
+   EXPECT_EQ(h->GetEntries(), h->GetEffectiveEntries());
+   delete h;
+   delete gROOT->FindObject("c1");
+}