diff --git a/src/iso19111/datum.cpp b/src/iso19111/datum.cpp
index 80dde967cd..8c89c2d70c 100644
--- a/src/iso19111/datum.cpp
+++ b/src/iso19111/datum.cpp
@@ -1557,9 +1557,14 @@ bool GeodeticReferenceFrame::_isEquivalentTo(
 bool GeodeticReferenceFrame::hasEquivalentNameToUsingAlias(
     const IdentifiedObject *other,
     const io::DatabaseContextPtr &dbContext) const {
-    if (nameStr() == "unknown" || other->nameStr() == "unknown") {
+    if (nameStr() == other->nameStr() || nameStr() == "unknown" ||
+        other->nameStr() == "unknown") {
         return true;
     }
+    if (ci_starts_with(nameStr(), UNKNOWN_BASED_ON) ||
+        ci_starts_with(other->nameStr(), UNKNOWN_BASED_ON)) {
+        return false;
+    }
     if (dbContext) {
         if (!identifiers().empty()) {
             const auto &id = identifiers().front();
diff --git a/src/iso19111/operation/coordinateoperationfactory.cpp b/src/iso19111/operation/coordinateoperationfactory.cpp
index 0e1f35c997..5ea611371b 100644
--- a/src/iso19111/operation/coordinateoperationfactory.cpp
+++ b/src/iso19111/operation/coordinateoperationfactory.cpp
@@ -1720,7 +1720,7 @@ void CoordinateOperationFactory::Private::buildCRSIds(
             }
         }
     }
-    if (ids.empty()) {
+    if (ids.empty() && !ci_equal(crs->nameStr(), "unknown")) {
         std::vector<io::AuthorityFactory::ObjectType> allowedObjects;
         auto geogCRS = dynamic_cast<const crs::GeographicCRS *>(crs.get());
         if (geogCRS) {
@@ -1810,6 +1810,13 @@ CoordinateOperationFactory::Private::findOpsInRegistryDirect(
     const auto &authFactory = context.context->getAuthorityFactory();
     assert(authFactory);
 
+    if ((sourceCRS->identifiers().empty() &&
+         ci_equal(sourceCRS->nameStr(), "unknown")) ||
+        (targetCRS->identifiers().empty() &&
+         ci_equal(targetCRS->nameStr(), "unknown"))) {
+        return {};
+    }
+
 #ifdef TRACE_CREATE_OPERATIONS
     ENTER_BLOCK("findOpsInRegistryDirect(" + objectAsStr(sourceCRS.get()) +
                 " --> " + objectAsStr(targetCRS.get()) + ")");
@@ -1991,21 +1998,39 @@ CoordinateOperationFactory::Private::findsOpsInRegistryWithIntermediate(
                 objectAsStr(sourceCRS.get()) + " --> " +
                 objectAsStr(targetCRS.get()) + ")");
 #endif
-
     const auto &authFactory = context.context->getAuthorityFactory();
     assert(authFactory);
 
+    const auto dbContext = authFactory->databaseContext().as_nullable();
+    const auto geodSrc = dynamic_cast<crs::GeodeticCRS *>(sourceCRS.get());
+    const auto datumSrc =
+        geodSrc ? geodSrc->datumNonNull(dbContext).as_nullable() : nullptr;
+    // Optimization: check if the source/target CRS have no chance to match
+    // a database entry
+    if (datumSrc && datumSrc->identifiers().empty() &&
+        (ci_equal(datumSrc->nameStr(), "unknown") ||
+         ci_starts_with(datumSrc->nameStr(), UNKNOWN_BASED_ON)))
+        return {};
+    if (!geodSrc && dynamic_cast<crs::BoundCRS *>(sourceCRS.get()))
+        return {};
+    const auto geodDst = dynamic_cast<crs::GeodeticCRS *>(targetCRS.get());
+    const auto datumDst =
+        geodDst ? geodDst->datumNonNull(dbContext).as_nullable() : nullptr;
+    if (datumDst && datumDst->identifiers().empty() &&
+        (ci_equal(datumDst->nameStr(), "unknown") ||
+         ci_starts_with(datumDst->nameStr(), UNKNOWN_BASED_ON)))
+        return {};
+    if (!geodDst && dynamic_cast<crs::BoundCRS *>(targetCRS.get()))
+        return {};
+
     std::list<std::pair<std::string, std::string>> sourceIds;
     buildCRSIds(sourceCRS, context, sourceIds);
     if (sourceIds.empty()) {
-        auto geodSrc = dynamic_cast<crs::GeodeticCRS *>(sourceCRS.get());
-        auto geodDst = dynamic_cast<crs::GeodeticCRS *>(targetCRS.get());
         if (geodSrc) {
             const std::string originatingAuthSrc =
                 geodSrc->getOriginatingAuthName();
-            const auto dbContext = authFactory->databaseContext().as_nullable();
             const auto candidatesSrcGeod(findCandidateGeodCRSForDatum(
-                authFactory, geodSrc, geodSrc->datumNonNull(dbContext)));
+                authFactory, geodSrc, NN_NO_CHECK(datumSrc)));
             std::vector<CoordinateOperationNNPtr> res;
             for (const auto &candidateSrcGeod : candidatesSrcGeod) {
                 // Restrict to using only objects that have the same authority
@@ -2022,11 +2047,11 @@ CoordinateOperationFactory::Private::findsOpsInRegistryWithIntermediate(
                      (dynamic_cast<crs::GeographicCRS *>(
                           candidateSrcGeod.get()) != nullptr))) {
                     if (geodDst) {
-                        const auto srcDatum =
+                        const auto candidateSrcDatum =
                             candidateSrcGeod->datumNonNull(dbContext);
-                        const auto dstDatum = geodDst->datumNonNull(dbContext);
-                        const bool sameGeodeticDatum =
-                            isSameGeodeticDatum(srcDatum, dstDatum, dbContext);
+                        const bool sameGeodeticDatum = isSameGeodeticDatum(
+                            candidateSrcDatum, NN_NO_CHECK(datumDst),
+                            dbContext);
                         if (sameGeodeticDatum) {
                             continue;
                         }
@@ -3078,10 +3103,21 @@ void CoordinateOperationFactory::Private::createOperationsWithDatumPivot(
     const auto &authFactory = context.context->getAuthorityFactory();
     const auto &dbContext = authFactory->databaseContext();
 
-    const auto candidatesSrcGeod(findCandidateGeodCRSForDatum(
-        authFactory, geodSrc, geodSrc->datumNonNull(dbContext.as_nullable())));
-    const auto candidatesDstGeod(findCandidateGeodCRSForDatum(
-        authFactory, geodDst, geodDst->datumNonNull(dbContext.as_nullable())));
+    const auto srcDatum = geodSrc->datumNonNull(dbContext.as_nullable());
+    if (srcDatum->identifiers().empty() &&
+        (ci_equal(srcDatum->nameStr(), "unknown") ||
+         ci_starts_with(srcDatum->nameStr(), UNKNOWN_BASED_ON)))
+        return;
+    const auto dstDatum = geodDst->datumNonNull(dbContext.as_nullable());
+    if (dstDatum->identifiers().empty() &&
+        (ci_equal(dstDatum->nameStr(), "unknown") ||
+         ci_starts_with(dstDatum->nameStr(), UNKNOWN_BASED_ON)))
+        return;
+
+    const auto candidatesSrcGeod(
+        findCandidateGeodCRSForDatum(authFactory, geodSrc, srcDatum));
+    const auto candidatesDstGeod(
+        findCandidateGeodCRSForDatum(authFactory, geodDst, dstDatum));
 
     const bool sourceAndTargetAre3D =
         geodSrc->coordinateSystem()->axisList().size() == 3 &&
diff --git a/test/unit/test_operationfactory.cpp b/test/unit/test_operationfactory.cpp
index 2cf5765ad3..e406834a81 100644
--- a/test/unit/test_operationfactory.cpp
+++ b/test/unit/test_operationfactory.cpp
@@ -684,10 +684,12 @@ TEST(operation, geogCRS_to_geogCRS_compatible_unknown_celestial_body) {
     auto srcCRS = nn_dynamic_pointer_cast<CRS>(objSrc);
     auto objDst =
         createFromUserInput("+proj=longlat +R=10001 +type=crs", dbContext);
+    const auto queryCounterBefore = dbContext->getQueryCounter();
     auto dstCRS = nn_dynamic_pointer_cast<CRS>(objDst);
     auto ctxt = CoordinateOperationContext::create(authFactory, nullptr, 0.0);
     auto list = CoordinateOperationFactory::create()->createOperations(
         NN_NO_CHECK(srcCRS), NN_NO_CHECK(dstCRS), ctxt);
+    EXPECT_EQ(dbContext->getQueryCounter(), queryCounterBefore);
     ASSERT_EQ(list.size(), 1U);
     EXPECT_EQ(list[0]->exportToPROJString(PROJStringFormatter::create().get()),
               "+proj=noop");
@@ -3063,11 +3065,13 @@ TEST(operation, createOperation_boundCRS_identified_by_datum) {
               "+ellps=clrk80ign +step +proj=pop +v_3 +step +proj=utm +zone=32 "
               "+ellps=clrk80ign");
 
-    auto authFactory =
-        AuthorityFactory::create(DatabaseContext::create(), std::string());
+    auto dbContext = DatabaseContext::create();
+    auto authFactory = AuthorityFactory::create(dbContext, std::string());
     auto ctxt = CoordinateOperationContext::create(authFactory, nullptr, 0.0);
+    const auto queryCounterBefore = dbContext->getQueryCounter();
     auto list = CoordinateOperationFactory::create()->createOperations(
         NN_CHECK_ASSERT(src), NN_CHECK_ASSERT(dest), ctxt);
+    EXPECT_EQ(dbContext->getQueryCounter(), queryCounterBefore);
     ASSERT_EQ(list.size(), 1U);
     EXPECT_TRUE(list[0]->isEquivalentTo(op.get()));
 }
@@ -3092,6 +3096,17 @@ TEST(operation, boundCRS_of_clrk_66_geogCRS_to_nad83_geogCRS) {
               "+proj=pipeline +step +proj=unitconvert +xy_in=deg +xy_out=rad "
               "+step +proj=hgridshift +grids=ntv1_can.dat,conus "
               "+step +proj=unitconvert +xy_in=rad +xy_out=deg");
+
+    auto dbContext = DatabaseContext::create();
+    auto authFactory = AuthorityFactory::create(dbContext, std::string());
+    auto ctxt = CoordinateOperationContext::create(authFactory, nullptr, 0.0);
+    const auto queryCounterBefore = dbContext->getQueryCounter();
+    auto list = CoordinateOperationFactory::create()->createOperations(
+        NN_CHECK_ASSERT(src), NN_CHECK_ASSERT(dest), ctxt);
+    // Two extra queries related to the conus grid
+    EXPECT_EQ(dbContext->getQueryCounter(), queryCounterBefore + 2);
+    ASSERT_EQ(list.size(), 1U);
+    EXPECT_TRUE(list[0]->isEquivalentTo(op.get()));
 }
 
 // ---------------------------------------------------------------------------