diff --git a/autotest/gdrivers/jpegxl.py b/autotest/gdrivers/jpegxl.py
index 27f21373acb8..4983e012b119 100755
--- a/autotest/gdrivers/jpegxl.py
+++ b/autotest/gdrivers/jpegxl.py
@@ -552,6 +552,24 @@ def test_jpegxl_write_five_bands():
     gdal.GetDriverByName("JPEGXL").Delete(outfilename)
 
 
+def test_jpegxl_write_five_bands_lossy():
+
+    drv = gdal.GetDriverByName("JPEGXL")
+    if drv.GetMetadataItem("JXL_ENCODER_SUPPORT_EXTRA_CHANNELS") is None:
+        pytest.skip()
+
+    src_ds = gdal.Open("data/jpegxl/five_bands.jxl")
+    outfilename = "/vsimem/out.jxl"
+    gdal.Translate(outfilename, src_ds, options="-of JPEGXL -co DISTANCE=3 -ot Byte")
+    ds = gdal.Open(outfilename)
+    for i in range(5):
+        assert ds.GetRasterBand(i + 1).ComputeRasterMinMax() == pytest.approx(
+            (10.0 * (i + 1), 10.0 * (i + 1)), abs=1
+        )
+    ds = None
+    gdal.GetDriverByName("JPEGXL").Delete(outfilename)
+
+
 def test_jpegxl_createcopy_errors():
 
     outfilename = "/vsimem/out.jxl"
diff --git a/doc/source/drivers/raster/jpegxl.rst b/doc/source/drivers/raster/jpegxl.rst
index 4ed85841b58f..f1453995c310 100644
--- a/doc/source/drivers/raster/jpegxl.rst
+++ b/doc/source/drivers/raster/jpegxl.rst
@@ -97,6 +97,8 @@ The following creation options are available:
       If set to NO, or in AUTO mode if the source dataset does not use JPEG
       compression, the regular conversion code path is taken, resulting in a
       lossless or lossy copy depending on the LOSSLESS setting.
+      AUTO mode defaults to NO, if EFFORT, DISTANCE, ALPHA_DISTANCE or QUALITY
+      options are used.
 
 -  .. co:: EFFORT
       :choices: 1-9
diff --git a/frmts/jpegxl/jpegxl.cpp b/frmts/jpegxl/jpegxl.cpp
index 0ac0f3e1925d..46befd797728 100644
--- a/frmts/jpegxl/jpegxl.cpp
+++ b/frmts/jpegxl/jpegxl.cpp
@@ -1798,16 +1798,35 @@ GDALDataset *JPEGXLDataset::CreateCopy(const char *pszFilename,
         }
     }
 
+    constexpr int DEFAULT_EFFORT = 5;
+    const int nEffort = atoi(CSLFetchNameValueDef(
+        papszOptions, "EFFORT", CPLSPrintf("%d", DEFAULT_EFFORT)));
+    const char *pszDistance = CSLFetchNameValue(papszOptions, "DISTANCE");
+    const char *pszQuality = CSLFetchNameValue(papszOptions, "QUALITY");
+    const char *pszAlphaDistance =
+        CSLFetchNameValue(papszOptions, "ALPHA_DISTANCE");
     const char *pszLossLessCopy =
         CSLFetchNameValueDef(papszOptions, "LOSSLESS_COPY", "AUTO");
-    if (EQUAL(pszLossLessCopy, "AUTO") || CPLTestBool(pszLossLessCopy))
+    if ((EQUAL(pszLossLessCopy, "AUTO") && !pszDistance && !pszQuality &&
+         !pszAlphaDistance && nEffort == DEFAULT_EFFORT) ||
+        (!EQUAL(pszLossLessCopy, "AUTO") && CPLTestBool(pszLossLessCopy)))
     {
         void *pJPEGXLContent = nullptr;
         size_t nJPEGXLContent = 0;
-        if (poSrcDS->ReadCompressedData(
-                "JXL", 0, 0, poSrcDS->GetRasterXSize(),
-                poSrcDS->GetRasterYSize(), poSrcDS->GetRasterCount(), nullptr,
-                &pJPEGXLContent, &nJPEGXLContent, nullptr) == CE_None)
+        const bool bSrcIsJXL =
+            (poSrcDS->ReadCompressedData(
+                 "JXL", 0, 0, poSrcDS->GetRasterXSize(),
+                 poSrcDS->GetRasterYSize(), poSrcDS->GetRasterCount(), nullptr,
+                 &pJPEGXLContent, &nJPEGXLContent, nullptr) == CE_None);
+        if (bSrcIsJXL && (pszDistance || pszQuality || pszAlphaDistance ||
+                          nEffort != DEFAULT_EFFORT))
+        {
+            CPLError(CE_Failure, CPLE_NotSupported,
+                     "LOSSLESS_COPY=YES not supported when EFFORT, QUALITY, "
+                     "DISTANCE or ALPHA_DISTANCE are specified");
+            return nullptr;
+        }
+        else if (bSrcIsJXL)
         {
             CPLDebug("JPEGXL", "Lossless copy from source dataset");
             GByte abySizeAndBoxName[8];
@@ -2062,10 +2081,6 @@ GDALDataset *JPEGXLDataset::CreateCopy(const char *pszFilename,
     }
 
     const char *pszLossLess = CSLFetchNameValue(papszOptions, "LOSSLESS");
-    const char *pszDistance = CSLFetchNameValue(papszOptions, "DISTANCE");
-    const char *pszQuality = CSLFetchNameValue(papszOptions, "QUALITY");
-    const char *pszAlphaDistance =
-        CSLFetchNameValue(papszOptions, "ALPHA_DISTANCE");
 
     const bool bLossless = (pszLossLess == nullptr && pszDistance == nullptr &&
                             pszQuality == nullptr) ||
@@ -2325,7 +2340,6 @@ GDALDataset *JPEGXLDataset::CreateCopy(const char *pszFilename,
         }
     }
 
-    const int nEffort = atoi(CSLFetchNameValueDef(papszOptions, "EFFORT", "5"));
 #ifdef HAVE_JxlEncoderFrameSettingsSetOption
     if (JxlEncoderFrameSettingsSetOption(opts, JXL_ENC_FRAME_SETTING_EFFORT,
                                          nEffort) != JXL_ENC_SUCCESS)
@@ -2572,6 +2586,17 @@ GDALDataset *JPEGXLDataset::CreateCopy(const char *pszFilename,
                     return nullptr;
                 }
             }
+            else if (!bLossless)
+            {
+                // By default libjxl applies lossless encoding for extra channels
+                if (JXL_ENC_SUCCESS !=
+                    JxlEncoderSetExtraChannelDistance(opts, nIndex, fDistance))
+                {
+                    CPLError(CE_Failure, CPLE_AppDefined,
+                             "JxlEncoderSetExtraChannelDistance failed");
+                    return nullptr;
+                }
+            }
 #endif
         }
     }