diff --git a/src/ol/renderer/webgl/TileLayer.js b/src/ol/renderer/webgl/TileLayer.js
index 1e3ad1ed14..16b3c3309e 100644
--- a/src/ol/renderer/webgl/TileLayer.js
+++ b/src/ol/renderer/webgl/TileLayer.js
@@ -97,6 +97,14 @@ function getRenderExtent(frameState, extent) {
       fromUserExtent(layerState.extent, frameState.viewState.projection)
     );
   }
+  const source =
+    /** {import("../../source/Tile.js").default} */ layerState.layer.getSource();
+  if (!source.getWrapX()) {
+    const gridExtent = source.tileGrid.getExtent();
+    if (gridExtent) {
+      extent = getIntersection(extent, gridExtent);
+    }
+  }
   return extent;
 }
 
@@ -236,11 +244,13 @@ class WebGLTileLayerRenderer extends WebGLLayerRenderer {
    * @return {boolean} Layer is ready to be rendered.
    */
   prepareFrameInternal(frameState) {
-    if (isEmpty(getRenderExtent(frameState, frameState.extent))) {
+    const layer = this.getLayer();
+    const source = layer.getSource();
+    if (!source) {
       return false;
     }
-    const source = this.getLayer().getSource();
-    if (!source) {
+
+    if (isEmpty(getRenderExtent(frameState, frameState.extent))) {
       return false;
     }
     return source.getState() === State.READY;
@@ -248,7 +258,7 @@ class WebGLTileLayerRenderer extends WebGLLayerRenderer {
 
   /**
    * @param {import("../../PluggableMap.js").FrameState} frameState Frame state.
-   * @param {import("../../extent.js").Extent} extent The extent.
+   * @param {import("../../extent.js").Extent} extent The extent to be rendered.
    * @param {number} z The zoom level.
    * @param {Object<number, Array<TileTexture>>} tileTexturesByZ The zoom level.
    */
@@ -341,10 +351,10 @@ class WebGLTileLayerRenderer extends WebGLLayerRenderer {
     this.preRender(gl, frameState);
 
     const viewState = frameState.viewState;
-    const extent = getRenderExtent(frameState, frameState.extent);
     const tileLayer = this.getLayer();
     const tileSource = tileLayer.getSource();
     const tileGrid = tileSource.getTileGridForProjection(viewState.projection);
+    const extent = getRenderExtent(frameState, frameState.extent);
     const z = tileGrid.getZForResolution(
       viewState.resolution,
       tileSource.zDirection
diff --git a/src/ol/source/DataTile.js b/src/ol/source/DataTile.js
index 903d3c0b35..5b3cf452c1 100644
--- a/src/ol/source/DataTile.js
+++ b/src/ol/source/DataTile.js
@@ -31,7 +31,7 @@ import {toPromise} from '../functions.js';
  * @property {boolean} [opaque=false] Whether the layer is opaque.
  * @property {import("./State.js").default} [state] The source state.
  * @property {number} [tilePixelRatio] Tile pixel ratio.
- * @property {boolean} [wrapX=true] Render tiles beyond the antimeridian.
+ * @property {boolean} [wrapX=false] Render tiles beyond the antimeridian.
  * @property {number} [transition] Transition time when fading in new tiles (in miliseconds).
  * @property {number} [bandCount=4] Number of bands represented in the data.
  */
diff --git a/src/ol/source/GeoTIFF.js b/src/ol/source/GeoTIFF.js
index 784cc28852..88b81a6657 100644
--- a/src/ol/source/GeoTIFF.js
+++ b/src/ol/source/GeoTIFF.js
@@ -300,6 +300,7 @@ function getMaxForDataType(array) {
  * @property {boolean} [opaque=false] Whether the layer is opaque.
  * @property {number} [transition=250] Duration of the opacity transition for rendering.
  * To disable the opacity transition, pass `transition: 0`.
+ * @property {boolean} [wrapX=false] Render tiles beyond the tile grid extent.
  */
 
 /**
@@ -318,6 +319,7 @@ class GeoTIFFSource extends DataTile {
       projection: null,
       opaque: options.opaque,
       transition: options.transition,
+      wrapX: options.wrapX,
     });
 
     /**
diff --git a/src/ol/source/Tile.js b/src/ol/source/Tile.js
index 8d9b16207f..03a8038b51 100644
--- a/src/ol/source/Tile.js
+++ b/src/ol/source/Tile.js
@@ -34,7 +34,7 @@ import {scale as scaleSize, toSize} from '../size.js';
  * @property {import("../proj.js").ProjectionLike} [projection] Projection.
  * @property {import("./State.js").default} [state] State.
  * @property {import("../tilegrid/TileGrid.js").default} [tileGrid] TileGrid.
- * @property {boolean} [wrapX=true] WrapX.
+ * @property {boolean} [wrapX=false] WrapX.
  * @property {number} [transition] Transition.
  * @property {string} [key] Key.
  * @property {number|import("../array.js").NearestDirectionFunction} [zDirection=0] ZDirection.
diff --git a/test/browser/spec/ol/source/GeoTIFF.test.js b/test/browser/spec/ol/source/GeoTIFF.test.js
index 2ad410dacf..778f965956 100644
--- a/test/browser/spec/ol/source/GeoTIFF.test.js
+++ b/test/browser/spec/ol/source/GeoTIFF.test.js
@@ -27,6 +27,29 @@ describe('ol/source/GeoTIFF', function () {
       expect(source.readMethod_).to.be('readRGB');
     });
 
+    it('defaults to wrapX: false', function () {
+      const source = new GeoTIFFSource({
+        sources: [
+          {
+            url: 'spec/ol/source/images/0-0-0.tif',
+          },
+        ],
+      });
+      expect(source.getWrapX()).to.be(false);
+    });
+
+    it('allows wrapX to be set', function () {
+      const source = new GeoTIFFSource({
+        wrapX: true,
+        sources: [
+          {
+            url: 'spec/ol/source/images/0-0-0.tif',
+          },
+        ],
+      });
+      expect(source.getWrapX()).to.be(true);
+    });
+
     it('generates Float32Array data if normalize is set to false', (done) => {
       const source = new GeoTIFFSource({
         normalize: false,
diff --git a/test/browser/spec/ol/webgl/TileTexture.test.js b/test/browser/spec/ol/webgl/TileTexture.test.js
index 3ad9a1bb19..e454a3c53c 100644
--- a/test/browser/spec/ol/webgl/TileTexture.test.js
+++ b/test/browser/spec/ol/webgl/TileTexture.test.js
@@ -7,6 +7,7 @@ import WebGLArrayBuffer from '../../../../../src/ol/webgl/Buffer.js';
 import WebGLTileLayer from '../../../../../src/ol/layer/WebGLTile.js';
 import {EXTENT as EPSG3857_EXTENT} from '../../../../../src/ol/proj/epsg3857.js';
 import {createCanvasContext2D} from '../../../../../src/ol/dom.js';
+import {get as getProjection} from '../../../../../src/ol/proj.js';
 
 describe('ol/webgl/TileTexture', function () {
   /** @type {TileTexture} */
@@ -31,6 +32,9 @@ describe('ol/webgl/TileTexture', function () {
 
     renderer = layer.createRenderer();
     renderer.prepareFrame({
+      viewState: {
+        projection: getProjection('EPSG:3857'),
+      },
       extent: EPSG3857_EXTENT,
       layerIndex: 0,
       layerStatesArray: [layer.getLayerState()],
diff --git a/test/rendering/cases/webgl-data-tile-no-wrap/expected.png b/test/rendering/cases/webgl-data-tile-no-wrap/expected.png
new file mode 100644
index 0000000000..df2b332db1
Binary files /dev/null and b/test/rendering/cases/webgl-data-tile-no-wrap/expected.png differ
diff --git a/test/rendering/cases/webgl-data-tile-no-wrap/main.js b/test/rendering/cases/webgl-data-tile-no-wrap/main.js
new file mode 100644
index 0000000000..3ea6865880
--- /dev/null
+++ b/test/rendering/cases/webgl-data-tile-no-wrap/main.js
@@ -0,0 +1,63 @@
+import DataTile from '../../../../src/ol/source/DataTile.js';
+import Map from '../../../../src/ol/Map.js';
+import TileLayer from '../../../../src/ol/layer/WebGLTile.js';
+import View from '../../../../src/ol/View.js';
+import XYZ from '../../../../src/ol/source/XYZ.js';
+
+const labelCanvasSize = 256;
+
+const labelCanvas = document.createElement('canvas');
+labelCanvas.width = labelCanvasSize;
+labelCanvas.height = labelCanvasSize;
+
+const labelContext = labelCanvas.getContext('2d');
+labelContext.textAlign = 'center';
+labelContext.font = '16px sans-serif';
+const labelLineHeight = 16;
+
+new Map({
+  layers: [
+    new TileLayer({
+      source: new XYZ({
+        url: '/data/tiles/satellite/{z}/{x}/{y}.jpg',
+        transition: 0,
+      }),
+    }),
+    new TileLayer({
+      source: new DataTile({
+        loader: function (z, x, y) {
+          const half = labelCanvasSize / 2;
+
+          labelContext.clearRect(0, 0, labelCanvasSize, labelCanvasSize);
+
+          labelContext.fillStyle = 'white';
+          labelContext.fillText(`z: ${z}`, half, half - labelLineHeight);
+          labelContext.fillText(`x: ${x}`, half, half);
+          labelContext.fillText(`y: ${y}`, half, half + labelLineHeight);
+
+          labelContext.strokeStyle = 'white';
+          labelContext.lineWidth = 2;
+          labelContext.strokeRect(0, 0, labelCanvasSize, labelCanvasSize);
+
+          const data = labelContext.getImageData(
+            0,
+            0,
+            labelCanvasSize,
+            labelCanvasSize
+          ).data;
+          return new Uint8Array(data.buffer);
+        },
+        transition: 0,
+      }),
+    }),
+  ],
+  target: 'map',
+  view: new View({
+    center: [15700000, 2700000],
+    zoom: 2,
+  }),
+});
+
+render({
+  message: 'data tiles outside the world are not rendered',
+});
diff --git a/test/rendering/cases/webgl-mixed-layers/main.js b/test/rendering/cases/webgl-mixed-layers/main.js
index 31f4e24f19..d35267d0b0 100644
--- a/test/rendering/cases/webgl-mixed-layers/main.js
+++ b/test/rendering/cases/webgl-mixed-layers/main.js
@@ -46,6 +46,7 @@ new Map({
     }),
     new TileLayer({
       source: new DataTile({
+        wrapX: true,
         loader: function (z, x, y) {
           const half = labelCanvasSize / 2;
 
diff --git a/test/rendering/cases/webgl-multiple-layers/main.js b/test/rendering/cases/webgl-multiple-layers/main.js
index d0021531e8..b7336d6f1d 100644
--- a/test/rendering/cases/webgl-multiple-layers/main.js
+++ b/test/rendering/cases/webgl-multiple-layers/main.js
@@ -44,6 +44,7 @@ new Map({
     }),
     new TileLayer({
       source: new DataTile({
+        wrapX: true,
         loader: function (z, x, y) {
           const half = labelCanvasSize / 2;