diff --git a/autotest/gcore/tiff_srs.py b/autotest/gcore/tiff_srs.py
index b5b08bc54c76..b5fe8d96d2af 100755
--- a/autotest/gcore/tiff_srs.py
+++ b/autotest/gcore/tiff_srs.py
@@ -1289,3 +1289,59 @@ def test_tiff_srs_read_compound_with_VerticalCitationGeoKey_only():
         wkt
         == """COMPD_CS["TestMS",GEOGCS["NAD83(2011)",DATUM["NAD83_National_Spatial_Reference_System_2011",SPHEROID["GRS 1980",6378137,298.257222101004,AUTHORITY["EPSG","7019"]],AUTHORITY["EPSG","1116"]],PRIMEM["Greenwich",0],UNIT["degree",0.0174532925199433,AUTHORITY["EPSG","9122"]],AXIS["Latitude",NORTH],AXIS["Longitude",EAST],AUTHORITY["EPSG","6318"]],VERT_CS["NAVD88 height",VERT_DATUM["North American Vertical Datum 1988",2005,AUTHORITY["EPSG","5103"]],UNIT["metre",1,AUTHORITY["EPSG","9001"]],AXIS["Up",UP]]]"""
     )
+
+
+@pytest.mark.parametrize(
+    "code",
+    [
+        7415,  # Amersfoort / RD New + NAP height
+        9707,  # WGS 84 + EGM96 height
+    ],
+)
+@pytest.mark.require_proj(
+    7, 2
+)  # not necessarily the minimum version, but 9707 doesn't exist in PROJ 6.x
+def test_tiff_srs_read_compound_with_EPSG_code(code):
+
+    """Test bugfix for https://github.com/OSGeo/gdal/issues/7982"""
+
+    filename = "/vsimem/test_tiff_srs_read_compound_with_EPSG_code.tif"
+    srs = osr.SpatialReference()
+    srs.ImportFromEPSG(code)
+    srs.SetAxisMappingStrategy(osr.OAMS_TRADITIONAL_GIS_ORDER)
+    ds = gdal.GetDriverByName("GTiff").Create(filename, 1, 1)
+    ds.SetSpatialRef(srs)
+    ds = None
+    ds = gdal.Open(filename)
+    gdal.ErrorReset()
+    got_srs = ds.GetSpatialRef()
+    assert gdal.GetLastErrorMsg() == "", srs.ExportToWkt(["FORMAT=WKT2_2019"])
+    assert got_srs.GetAuthorityCode(None) == str(code)
+    assert got_srs.IsSame(srs)
+    ds = None
+    gdal.Unlink(filename)
+
+
+def test_tiff_srs_read_compound_without_EPSG_code():
+
+    """Test case where identification of code for CompoundCRS (added for
+    bugfix of https://github.com/OSGeo/gdal/issues/7982) doesn't trigger"""
+
+    filename = "/vsimem/test_tiff_srs_read_compound_without_EPSG_code.tif"
+    srs = osr.SpatialReference()
+    # WGS 84 + NAP height, unlikely to have a EPSG code ever
+    srs.SetFromUserInput("EPSG:4326+5709")
+    srs.SetAxisMappingStrategy(osr.OAMS_TRADITIONAL_GIS_ORDER)
+    ds = gdal.GetDriverByName("GTiff").Create(filename, 1, 1)
+    ds.SetSpatialRef(srs)
+    ds = None
+    ds = gdal.Open(filename)
+    gdal.ErrorReset()
+    got_srs = ds.GetSpatialRef()
+    assert gdal.GetLastErrorMsg() == "", srs.ExportToWkt(["FORMAT=WKT2_2019"])
+    assert got_srs.GetAuthorityCode(None) is None
+    assert got_srs.GetAuthorityCode("GEOGCS") == "4326"
+    assert got_srs.GetAuthorityCode("VERT_CS") == "5709"
+    assert got_srs.IsSame(srs)
+    ds = None
+    gdal.Unlink(filename)
diff --git a/frmts/gtiff/gt_wkt_srs.cpp b/frmts/gtiff/gt_wkt_srs.cpp
index 488874b1c820..7895aaf6d2f0 100644
--- a/frmts/gtiff/gt_wkt_srs.cpp
+++ b/frmts/gtiff/gt_wkt_srs.cpp
@@ -1689,6 +1689,8 @@ OGRSpatialReferenceH GTIFGetOGISDefnAsOSR(GTIF *hGTIF, GTIFDefn *psDefn)
 
         if (bCanBuildCompoundCRS)
         {
+            const bool bHorizontalHasCode =
+                oSRS.GetAuthorityCode(nullptr) != nullptr;
             const char *pszHorizontalName = oSRS.GetName();
             const std::string osHorizontalName(
                 pszHorizontalName ? pszHorizontalName : "unnamed");
@@ -1735,6 +1737,19 @@ OGRSpatialReferenceH GTIFGetOGISDefnAsOSR(GTIF *hGTIF, GTIFDefn *psDefn)
             {
                 oSRS.GetRoot()->AddChild(oVertSRS.GetRoot()->Clone());
                 bNeedManualVertCS = false;
+
+                // GeoTIFF doesn't store EPSG code of CompoundCRS, so
+                // if we have an EPSG code for both the horizontal and vertical
+                // parts, check if there's a known CompoundCRS associating
+                // both
+                if (bHorizontalHasCode && verticalCSType != KvUserDefined &&
+                    verticalCSType > 0)
+                {
+                    const auto *poSRSMatch = oSRS.FindBestMatch(100);
+                    if (poSRSMatch)
+                        oSRS = *poSRSMatch;
+                    delete poSRSMatch;
+                }
             }
         }
     }