diff --git a/src/iso19111/operation/singleoperation.cpp b/src/iso19111/operation/singleoperation.cpp
index 354975d386..031327c0f5 100644
--- a/src/iso19111/operation/singleoperation.cpp
+++ b/src/iso19111/operation/singleoperation.cpp
@@ -3545,7 +3545,11 @@ bool SingleOperation::exportToPROJStringGeneric(
             ((sourceCRSGeog &&
               sourceCRSGeog->coordinateSystem()->axisList().size() == 2) ||
              (targetCRSGeog &&
-              targetCRSGeog->coordinateSystem()->axisList().size() == 2));
+              targetCRSGeog->coordinateSystem()->axisList().size() == 2)) ||
+            (!sourceCRSGeog &&
+             dynamic_cast<const crs::CompoundCRS *>(l_sourceCRS.get())) ||
+            (!targetCRSGeog &&
+             dynamic_cast<const crs::CompoundCRS *>(l_targetCRS.get()));
 
         if (l_sourceCRS) {
             setupPROJGeodeticSourceCRS(formatter, NN_NO_CHECK(l_sourceCRS),
diff --git a/test/unit/test_operationfactory.cpp b/test/unit/test_operationfactory.cpp
index e406834a81..ad38690999 100644
--- a/test/unit/test_operationfactory.cpp
+++ b/test/unit/test_operationfactory.cpp
@@ -5954,6 +5954,44 @@ TEST(operation,
 
 // ---------------------------------------------------------------------------
 
+TEST(operation, compoundCRS_to_compoundCRS_context_helmert) {
+    auto dbContext = DatabaseContext::create();
+    auto authFactory = AuthorityFactory::create(dbContext, "EPSG");
+    auto ctxt = CoordinateOperationContext::create(authFactory, nullptr, 0.0);
+    ctxt->setGridAvailabilityUse(
+        CoordinateOperationContext::GridAvailabilityUse::
+            IGNORE_GRID_AVAILABILITY);
+    ctxt->setSpatialCriterion(
+        CoordinateOperationContext::SpatialCriterion::PARTIAL_INTERSECTION);
+    // GDA94 + AHD height
+    auto objSrc = createFromUserInput("EPSG:9464", dbContext);
+    auto srcCrs = nn_dynamic_pointer_cast<CompoundCRS>(objSrc);
+    ASSERT_TRUE(srcCrs != nullptr);
+    // GDA2020 + AHD height
+    auto objDest = createFromUserInput("EPSG:9463", dbContext);
+    auto destCrs = nn_dynamic_pointer_cast<CompoundCRS>(objDest);
+    ASSERT_TRUE(destCrs != nullptr);
+    auto list = CoordinateOperationFactory::create()->createOperations(
+        NN_NO_CHECK(srcCrs), NN_NO_CHECK(destCrs), ctxt);
+    ASSERT_GE(list.size(), 1U);
+    // Check presence of push/pop v_3
+    EXPECT_EQ(list[0]->exportToPROJString(PROJStringFormatter::create().get()),
+              "+proj=pipeline "
+              "+step +proj=axisswap +order=2,1 "
+              "+step +proj=unitconvert +xy_in=deg +xy_out=rad "
+              "+step +proj=push +v_3 "
+              "+step +proj=cart +ellps=GRS80 "
+              "+step +proj=helmert +x=0.06155 +y=-0.01087 +z=-0.04019 "
+              "+rx=-0.0394924 +ry=-0.0327221 +rz=-0.0328979 +s=-0.009994 "
+              "+convention=coordinate_frame "
+              "+step +inv +proj=cart +ellps=GRS80 "
+              "+step +proj=pop +v_3 "
+              "+step +proj=unitconvert +xy_in=rad +xy_out=deg "
+              "+step +proj=axisswap +order=2,1");
+}
+
+// ---------------------------------------------------------------------------
+
 TEST(
     operation,
     compoundCRS_to_compoundCRS_concatenated_operation_with_two_vert_transformation) {