diff --git a/frmts/vrt/vrtsources.cpp b/frmts/vrt/vrtsources.cpp
index 26a5e468d58a..bc7a8f6b9a37 100644
--- a/frmts/vrt/vrtsources.cpp
+++ b/frmts/vrt/vrtsources.cpp
@@ -3080,6 +3080,52 @@ static inline bool hasZeroByte(uint32_t v)
     return (((v)-0x01010101U) & ~(v)&0x80808080U) != 0;
 }
 
+/************************************************************************/
+/*                                CopyWord()                            */
+/************************************************************************/
+
+template <class SrcType>
+static void CopyWord(const SrcType *pSrcVal, GDALDataType eSrcType,
+                     void *pDstVal, GDALDataType eDstType)
+{
+    switch (eDstType)
+    {
+        case GDT_Byte:
+            GDALCopyWord(*pSrcVal, *static_cast<uint8_t *>(pDstVal));
+            break;
+        case GDT_Int8:
+            GDALCopyWord(*pSrcVal, *static_cast<int8_t *>(pDstVal));
+            break;
+        case GDT_UInt16:
+            GDALCopyWord(*pSrcVal, *static_cast<uint16_t *>(pDstVal));
+            break;
+        case GDT_Int16:
+            GDALCopyWord(*pSrcVal, *static_cast<int16_t *>(pDstVal));
+            break;
+        case GDT_UInt32:
+            GDALCopyWord(*pSrcVal, *static_cast<uint32_t *>(pDstVal));
+            break;
+        case GDT_Int32:
+            GDALCopyWord(*pSrcVal, *static_cast<int32_t *>(pDstVal));
+            break;
+        case GDT_UInt64:
+            GDALCopyWord(*pSrcVal, *static_cast<uint64_t *>(pDstVal));
+            break;
+        case GDT_Int64:
+            GDALCopyWord(*pSrcVal, *static_cast<int64_t *>(pDstVal));
+            break;
+        case GDT_Float32:
+            GDALCopyWord(*pSrcVal, *static_cast<float *>(pDstVal));
+            break;
+        case GDT_Float64:
+            GDALCopyWord(*pSrcVal, *static_cast<double *>(pDstVal));
+            break;
+        default:
+            GDALCopyWords(pSrcVal, eSrcType, 0, pDstVal, eDstType, 0, 1);
+            break;
+    }
+}
+
 /************************************************************************/
 /*                       RasterIOProcessNoData()                        */
 /************************************************************************/
@@ -3235,8 +3281,8 @@ CPLErr VRTComplexSource::RasterIOProcessNoData(
             {
                 if (paSrcData[idxBuffer] != nNoDataValue)
                 {
-                    GDALCopyWords(&paSrcData[idxBuffer], eSourceType, 0,
-                                  pDstLocation, eBufType, 0, 1);
+                    CopyWord(&paSrcData[idxBuffer], eSourceType, pDstLocation,
+                             eBufType);
                 }
             }
         }
@@ -3256,8 +3302,8 @@ CPLErr VRTComplexSource::RasterIOProcessNoData(
                 {
                     // Convert first to the VRTRasterBand data type
                     // to get its clamping, before outputting to buffer data type
-                    GDALCopyWords(&paSrcData[idxBuffer], eSourceType, 0,
-                                  abyTemp, eVRTBandDataType, 0, 1);
+                    CopyWord(&paSrcData[idxBuffer], eSourceType, abyTemp,
+                             eVRTBandDataType);
                     GDALCopyWords(abyTemp, eVRTBandDataType, 0, pDstLocation,
                                   eBufType, 0, 1);
                 }
@@ -3415,6 +3461,12 @@ CPLErr VRTComplexSource::RasterIOInternal(
     /*      Selectively copy into output buffer with nodata masking,        */
     /*      and/or scaling.                                                 */
     /* -------------------------------------------------------------------- */
+
+    const bool bTwoStepDataTypeConversion =
+        CPL_TO_BOOL(
+            GDALDataTypeIsConversionLossy(eWrkDataType, eVRTBandDataType)) &&
+        !CPL_TO_BOOL(GDALDataTypeIsConversionLossy(eVRTBandDataType, eBufType));
+
     size_t idxBuffer = 0;
     for (int iY = 0; iY < nOutYSize; iY++)
     {
@@ -3551,18 +3603,28 @@ CPLErr VRTComplexSource::RasterIOInternal(
                     255.0f,
                     std::max(0.0f, static_cast<float>(afResult[0]) + 0.5f)));
             }
-            else if (eBufType == eVRTBandDataType)
+            else if (!bTwoStepDataTypeConversion)
+            {
+                CopyWord<WorkingDT>(afResult, eWrkDataType, pDstLocation,
+                                    eBufType);
+            }
+            else if (eVRTBandDataType == GDT_Float32 && eBufType == GDT_Float64)
             {
-                GDALCopyWords(afResult, eWrkDataType, 0, pDstLocation, eBufType,
-                              0, 1);
+                // Particular case of the below 2-step conversion.
+                // Helps a bit for some geolocation based warping with Sentinel3
+                // data where the longitude/latitude arrays are Int32 bands,
+                // rescaled in VRT as Float32 and requested as Float64
+                float fVal;
+                GDALCopyWord(afResult[0], fVal);
+                *reinterpret_cast<double *>(pDstLocation) = fVal;
             }
             else
             {
                 GByte abyTemp[2 * sizeof(double)];
                 // Convert first to the VRTRasterBand data type
                 // to get its clamping, before outputting to buffer data type
-                GDALCopyWords(afResult, eWrkDataType, 0, abyTemp,
-                              eVRTBandDataType, 0, 1);
+                CopyWord<WorkingDT>(afResult, eWrkDataType, abyTemp,
+                                    eVRTBandDataType);
                 GDALCopyWords(abyTemp, eVRTBandDataType, 0, pDstLocation,
                               eBufType, 0, 1);
             }