diff --git a/roofit/roofitcore/src/RooProdPdf.cxx b/roofit/roofitcore/src/RooProdPdf.cxx
index 2538a4c7bf88a..ee9095ec71449 100644
--- a/roofit/roofitcore/src/RooProdPdf.cxx
+++ b/roofit/roofitcore/src/RooProdPdf.cxx
@@ -2061,6 +2061,41 @@ RooProdPdf::compileForNormSet(RooArgSet const &normSet, RooFit::Detail::CompileC
    std::unique_ptr<RooProdPdf> prodPdfClone{static_cast<RooProdPdf *>(this->Clone())};
    ctx.markAsCompiled(*prodPdfClone);
 
+   // If this RooProdPdf has a normalization range (e.g. the fit range in a
+   // ranged fit), propagate it to the component pdfs while they are compiled.
+   // This is required so that a RooAddPdf nested in a RooProdPdf reinterprets
+   // its coefficients with respect to the full range, exactly like a top-level
+   // RooAddPdf would. Without this, e.g. a RooProdPdf wrapping an extended
+   // RooAddPdf (a very common way to attach constraint terms) gives a different
+   // yield than the bare RooAddPdf in a ranged fit (GitHub issue #16673).
+   //
+   // The range must only be set on components for which it is actually defined:
+   // constraint pdfs of nuisance parameters are normalized over observables that
+   // don't know about the fit range, and forcing it on them would be wrong (and
+   // for a multi-range even throws because the undefined sub-ranges collapse to
+   // the full range and overlap).
+   std::vector<std::pair<RooAbsPdf *, std::string>> restoreNormRanges;
+   if (const char *prodNormRange = normRange()) {
+      std::vector<std::string> rangeTokens = ROOT::Split(prodNormRange, ",", /*skipEmpty=*/true);
+      for (auto *pdf : static_range_cast<RooAbsPdf *>(prodPdfClone->_pdfList)) {
+         RooArgSet pdfObs;
+         pdf->getObservables(&normSet, pdfObs);
+         bool rangeDefined = !pdfObs.empty();
+         for (RooAbsArg *obs : pdfObs) {
+            auto *lval = dynamic_cast<RooAbsRealLValue *>(obs);
+            for (auto const &token : rangeTokens) {
+               if (!lval || !lval->hasRange(token.c_str())) {
+                  rangeDefined = false;
+               }
+            }
+         }
+         if (rangeDefined && std::string(pdf->normRange() ? pdf->normRange() : "") != prodNormRange) {
+            restoreNormRanges.emplace_back(pdf, pdf->normRange() ? pdf->normRange() : "");
+            pdf->setNormRange(prodNormRange);
+         }
+      }
+   }
+
    for (const auto server : prodPdfClone->servers()) {
       auto nsetForServer = fillNormSetForServer(normSet, *server);
       RooArgSet const &nset = nsetForServer ? *nsetForServer : normSet;
@@ -2071,6 +2106,10 @@ RooProdPdf::compileForNormSet(RooArgSet const &normSet, RooFit::Detail::CompileC
       ctx.compileServer(*server, *prodPdfClone, depList);
    }
 
+   for (auto const &[pdf, oldRange] : restoreNormRanges) {
+      pdf->setNormRange(oldRange.empty() ? nullptr : oldRange.c_str());
+   }
+
    auto fixedProdPdf = std::make_unique<RooFit::Detail::RooFixedProdPdf>(std::move(prodPdfClone), normSet);
    ctx.markAsCompiled(*fixedProdPdf);
 
diff --git a/roofit/roofitcore/test/testRooProdPdf.cxx b/roofit/roofitcore/test/testRooProdPdf.cxx
index 2b7d0cbd9dfed..c32d97fecf680 100644
--- a/roofit/roofitcore/test/testRooProdPdf.cxx
+++ b/roofit/roofitcore/test/testRooProdPdf.cxx
@@ -13,6 +13,7 @@
 #include <RooRealVar.h>
 #include <RooWorkspace.h>
 #include <RooHelpers.h>
+#include <RooRandom.h>
 
 #include <Math/PdfFuncMathCore.h>
 
@@ -248,3 +249,65 @@ TEST(RooProdPdf, RooProdPdfWithExtendedTerm)
    double nll1Val = nll1->getVal();
    EXPECT_FLOAT_EQ(nll1Val, refVal);
 }
+
+// A RooProdPdf that just wraps a (extended) RooAddPdf must give the same result
+// in a ranged fit as the bare RooAddPdf. In particular, the RooAddPdf yield must
+// be reinterpreted with respect to the full range in both cases. This is the
+// common workspace pattern of attaching constraint terms to a model via a
+// RooProdPdf. Regression test for GitHub issue #16673.
+TEST(RooProdPdf, RangedFitWrappingRooAddPdf)
+{
+   using namespace RooFit;
+   RooHelpers::LocalChangeMsgLevel changeMsgLvl(RooFit::WARNING);
+
+   RooRandom::randomGenerator()->SetSeed(42);
+
+   RooRealVar x("x", "x", 0, 100);
+   x.setRange("LEFT", 0, 20);
+   x.setRange("RIGHT", 60, 100);
+
+   RooRealVar alphaGen("alpha", "alpha", -0.04, -0.1, -0.0);
+   RooGenericPdf modelGen("model", "exp(alpha*x)", {x, alphaGen});
+   std::unique_ptr<RooDataSet> data{modelGen.generate(x, 10000)};
+
+   // A nuisance parameter with a Gaussian constraint. Its observable does not
+   // know about the "LEFT"/"RIGHT" ranges, so the fit range must not be forced
+   // onto the constraint pdf (otherwise the ranged normalization throws).
+   RooRealVar theta("theta", "theta", 0, -5, 5);
+   RooRealVar thetaGlob("thetaGlob", "thetaGlob", 0);
+   RooRealVar thetaErr("thetaErr", "thetaErr", 1.0);
+   RooGenericPdf constraint("constraint", "exp(-0.5*(theta-thetaGlob)^2/thetaErr^2)", {theta, thetaGlob, thetaErr});
+
+   auto fitYield = [&](bool wrapInProd, bool withConstraint) {
+      RooRealVar alpha("alpha", "alpha", -0.04, -0.1, -0.0);
+      RooGenericPdf model("model", "exp(alpha*x)", {x, alpha});
+      RooRealVar nBkg("Nbkg", "Nbkg", 10000, 0, 20000);
+      RooAddPdf add("pdfadd", "", RooArgList{model}, RooArgList{nBkg});
+      std::unique_ptr<RooAbsPdf> owned;
+      RooAbsPdf *pdf = &add;
+      if (wrapInProd) {
+         RooArgList factors{add};
+         if (withConstraint) {
+            factors.add(constraint);
+         }
+         owned = std::make_unique<RooProdPdf>("pdfprod", "", factors);
+         pdf = owned.get();
+      }
+      pdf->fitTo(*data, Range("LEFT,RIGHT"), PrintLevel(-1));
+      return nBkg.getVal();
+   };
+
+   const double yieldAdd = fitYield(false, false);
+   const double yieldProd = fitYield(true, false);
+   const double yieldProdConstr = fitYield(true, true);
+
+   // The yield must refer to the full range, i.e. be clearly larger than the
+   // number of events actually inside the fit range.
+   const double nInFitRange = std::unique_ptr<RooAbsData>{data->reduce(CutRange("LEFT,RIGHT"))}->sumEntries();
+   EXPECT_GT(yieldAdd, 1.2 * nInFitRange);
+
+   // Wrapping in a RooProdPdf (with or without a constraint term) must not
+   // change the fitted yield.
+   EXPECT_NEAR(yieldProd, yieldAdd, 1e-3 * yieldAdd);
+   EXPECT_NEAR(yieldProdConstr, yieldAdd, 1e-3 * yieldAdd);
+}