diff --git a/effects/logout/logout.cpp b/effects/logout/logout.cpp
index 59c078becc..34fa81d024 100644
--- a/effects/logout/logout.cpp
+++ b/effects/logout/logout.cpp
@@ -109,7 +109,10 @@ void LogoutEffect::prePaintScreen(ScreenPrePaintData& data, int time)
             // TODO: It seems that it is not possible to create a GLRenderTarget that has
             //       a different size than the display right now. Most likely a KWin core bug.
             // Create texture and render target
-            blurTexture = new GLTexture(effects->virtualScreenSize());
+            const QSize size = effects->virtualScreenSize();
+
+            // The fragment shader uses a LOD bias of 1.75, so we need 3 mipmap levels.
+            blurTexture = new GLTexture(size, 3);
             blurTexture->setFilter(GL_LINEAR_MIPMAP_LINEAR);
             blurTexture->setWrapMode(GL_CLAMP_TO_EDGE);
 
diff --git a/effects/lookingglass/lookingglass.cpp b/effects/lookingglass/lookingglass.cpp
index 784b303a66..e6b5c83316 100644
--- a/effects/lookingglass/lookingglass.cpp
+++ b/effects/lookingglass/lookingglass.cpp
@@ -35,6 +35,8 @@ along with this program.  If not, see <http://www.gnu.org/licenses/>.
 
 #include <kmessagebox.h>
 
+#include <cmath>
+
 namespace KWin
 {
 
@@ -99,7 +101,8 @@ bool LookingGlassEffect::loadData()
     int texh = screenSize.height();
 
     // Create texture and render target
-    m_texture = new GLTexture(texw, texh);
+    const int levels = std::log2(qMin(texw, texh)) + 1;
+    m_texture = new GLTexture(texw, texh, levels);
     m_texture->setFilter(GL_LINEAR_MIPMAP_LINEAR);
     m_texture->setWrapMode(GL_CLAMP_TO_EDGE);
 
diff --git a/libkwineffects/kwingltexture.cpp b/libkwineffects/kwingltexture.cpp
index 8eb8a82984..beed208232 100644
--- a/libkwineffects/kwingltexture.cpp
+++ b/libkwineffects/kwingltexture.cpp
@@ -77,15 +77,15 @@ GLTexture::GLTexture(const QImage& image, GLenum target)
     if (d->m_target != GL_TEXTURE_RECTANGLE_ARB) {
         d->m_scale.setWidth(1.0 / image.width());
         d->m_scale.setHeight(1.0 / image.height());
-        d->m_canUseMipmaps = true;
     } else {
         d->m_scale.setWidth(1.0);
         d->m_scale.setHeight(1.0);
-        d->m_canUseMipmaps = false;
     }
 
     d->m_size = image.size();
     d->m_yInverted = true;
+    d->m_canUseMipmaps = false;
+    d->m_mipLevels = 1;
 
     d->updateMatrix();
 
@@ -94,6 +94,7 @@ GLTexture::GLTexture(const QImage& image, GLenum target)
 
     if (!GLPlatform::instance()->isGLES()) {
         const QImage im = image.convertToFormat(QImage::Format_ARGB32_Premultiplied);
+        glTexParameteri(d->m_target, GL_TEXTURE_MAX_LEVEL, d->m_mipLevels - 1);
         glTexImage2D(d->m_target, 0, GL_RGBA8, im.width(), im.height(), 0,
                      GL_BGRA, GL_UNSIGNED_INT_8_8_8_8_REV, im.bits());
     } else {
@@ -122,7 +123,7 @@ GLTexture::GLTexture(const QString& fileName)
 {
 }
 
-GLTexture::GLTexture(int width, int height)
+GLTexture::GLTexture(int width, int height, int levels)
      : d_ptr(new GLTexturePrivate())
 {
     Q_D(GLTexture);
@@ -131,7 +132,10 @@ GLTexture::GLTexture(int width, int height)
     d->m_scale.setWidth(1.0 / width);
     d->m_scale.setHeight(1.0 / height);
     d->m_size = QSize(width, height);
+    d->m_canUseMipmaps = levels > 1;
+    d->m_mipLevels = levels;
     d->m_canUseMipmaps = true;
+    d->m_filter = levels > 1 ? GL_NEAREST_MIPMAP_LINEAR : GL_NEAREST;
 
     d->updateMatrix();
 
@@ -139,6 +143,7 @@ GLTexture::GLTexture(int width, int height)
     bind();
 
     if (!GLPlatform::instance()->isGLES()) {
+        glTexParameteri(d->m_target, GL_TEXTURE_MAX_LEVEL, levels - 1);
         glTexImage2D(d->m_target, 0, GL_RGBA8, width, height, 0,
                      GL_BGRA, GL_UNSIGNED_INT_8_8_8_8_REV, nullptr);
     } else {
@@ -153,8 +158,8 @@ GLTexture::GLTexture(int width, int height)
     unbind();
 }
 
-GLTexture::GLTexture(const QSize &size)
-    : GLTexture(size.width(), size.height())
+GLTexture::GLTexture(const QSize &size, int levels)
+    : GLTexture(size.width(), size.height(), levels)
 {
 }
 
@@ -176,6 +181,7 @@ GLTexturePrivate::GLTexturePrivate()
     m_wrapMode = GL_REPEAT;
     m_yInverted = false;
     m_canUseMipmaps = false;
+    m_mipLevels = 1;
     m_markedDirty = false;
     m_unnormalizeActive = 0;
     m_normalizeActive = 0;
diff --git a/libkwineffects/kwingltexture.h b/libkwineffects/kwingltexture.h
index d559ab0bbe..3b9b012977 100644
--- a/libkwineffects/kwingltexture.h
+++ b/libkwineffects/kwingltexture.h
@@ -55,8 +55,8 @@ public:
     explicit GLTexture(const QImage& image, GLenum target = GL_TEXTURE_2D);
     explicit GLTexture(const QPixmap& pixmap, GLenum target = GL_TEXTURE_2D);
     explicit GLTexture(const QString& fileName);
-    GLTexture(int width, int height);
-    explicit GLTexture(const QSize &size);
+    GLTexture(int width, int height, int levels = 1);
+    explicit GLTexture(const QSize &size, int levels = 1);
     virtual ~GLTexture();
 
     GLTexture & operator = (const GLTexture& tex);
diff --git a/libkwineffects/kwingltexture_p.h b/libkwineffects/kwingltexture_p.h
index 3cbb0bb12e..d44b20d698 100644
--- a/libkwineffects/kwingltexture_p.h
+++ b/libkwineffects/kwingltexture_p.h
@@ -58,6 +58,7 @@ public:
     bool m_markedDirty;
     bool m_filterChanged;
     bool m_wrapModeChanged;
+    int m_mipLevels;
 
     int m_unnormalizeActive; // 0 - no, otherwise refcount
     int m_normalizeActive; // 0 - no, otherwise refcount