diff --git a/python/gui/qgsmaplayercombobox.sip b/python/gui/qgsmaplayercombobox.sip
index 475cee12c78..c14b53e927b 100644
--- a/python/gui/qgsmaplayercombobox.sip
+++ b/python/gui/qgsmaplayercombobox.sip
@@ -23,7 +23,7 @@ class QgsMapLayerComboBox : QComboBox
     QgsMapLayerProxyModel::Filters filters() const;
 
     //! currentLayer returns the current layer selected in the combo box
-    QgsMapLayer* currentLayer();
+    QgsMapLayer* currentLayer() const;
 
   public slots:
     //! setLayer set the current layer selected in the combo
diff --git a/python/gui/qgsmaplayermodel.sip b/python/gui/qgsmaplayermodel.sip
index d7f7d0a02ad..4f5e98ebdd2 100644
--- a/python/gui/qgsmaplayermodel.sip
+++ b/python/gui/qgsmaplayermodel.sip
@@ -37,12 +37,12 @@ class QgsMapLayerModel : QAbstractItemModel
      */
     QList<QgsMapLayer*> layersChecked( Qt::CheckState checkState = Qt::Checked );
     //! returns if the items can be checked or not
-    bool itemsCheckable();
+    bool itemsCheckable() const;
 
     /**
      * @brief indexFromLayer returns the model index for a given layer
      */
-    QModelIndex indexFromLayer( QgsMapLayer* layer );
+    QModelIndex indexFromLayer( QgsMapLayer* layer ) const;
 
 
   protected slots:
diff --git a/python/gui/qgsmaplayerproxymodel.sip b/python/gui/qgsmaplayerproxymodel.sip
index 9660f612e21..2f423dae0c5 100644
--- a/python/gui/qgsmaplayerproxymodel.sip
+++ b/python/gui/qgsmaplayerproxymodel.sip
@@ -33,7 +33,7 @@ class QgsMapLayerProxyModel : QSortFilterProxyModel
     /**
      * @brief layerModel returns the QgsMapLayerModel used in this QSortFilterProxyModel
      */
-    QgsMapLayerModel* sourceLayerModel();
+    QgsMapLayerModel* sourceLayerModel() const;
 
     /**
      * @brief setFilters set flags that affect how layers are filtered
diff --git a/src/gui/qgsmaplayercombobox.cpp b/src/gui/qgsmaplayercombobox.cpp
index 01eb0065344..f4856ce9d08 100644
--- a/src/gui/qgsmaplayercombobox.cpp
+++ b/src/gui/qgsmaplayercombobox.cpp
@@ -48,7 +48,7 @@ void QgsMapLayerComboBox::setLayer( QgsMapLayer *layer )
   emit layerChanged( currentLayer() );
 }
 
-QgsMapLayer* QgsMapLayerComboBox::currentLayer()
+QgsMapLayer* QgsMapLayerComboBox::currentLayer() const
 {
   int i = currentIndex();
 
diff --git a/src/gui/qgsmaplayercombobox.h b/src/gui/qgsmaplayercombobox.h
index 8d5648af6cb..c221cec23cd 100644
--- a/src/gui/qgsmaplayercombobox.h
+++ b/src/gui/qgsmaplayercombobox.h
@@ -47,7 +47,7 @@ class GUI_EXPORT QgsMapLayerComboBox : public QComboBox
     QgsMapLayerProxyModel::Filters filters() const { return mProxyModel->filters(); }
 
     //! currentLayer returns the current layer selected in the combo box
-    QgsMapLayer* currentLayer();
+    QgsMapLayer* currentLayer() const;
 
   public slots:
     //! setLayer set the current layer selected in the combo
diff --git a/src/gui/qgsmaplayermodel.cpp b/src/gui/qgsmaplayermodel.cpp
index 1e0b212b0c0..9e052eaf6fc 100644
--- a/src/gui/qgsmaplayermodel.cpp
+++ b/src/gui/qgsmaplayermodel.cpp
@@ -70,7 +70,7 @@ QList<QgsMapLayer *> QgsMapLayerModel::layersChecked( Qt::CheckState checkState
   return layers;
 }
 
-QModelIndex QgsMapLayerModel::indexFromLayer( QgsMapLayer *layer )
+QModelIndex QgsMapLayerModel::indexFromLayer( QgsMapLayer *layer ) const
 {
   int r = mLayers.indexOf( layer );
   return index( r, 0 );
diff --git a/src/gui/qgsmaplayermodel.h b/src/gui/qgsmaplayermodel.h
index 4bad6af8776..f2bfc8a9adb 100644
--- a/src/gui/qgsmaplayermodel.h
+++ b/src/gui/qgsmaplayermodel.h
@@ -57,12 +57,12 @@ class GUI_EXPORT QgsMapLayerModel : public QAbstractItemModel
      */
     QList<QgsMapLayer*> layersChecked( Qt::CheckState checkState = Qt::Checked );
     //! returns if the items can be checked or not
-    bool itemsCheckable() { return mItemCheckable; }
+    bool itemsCheckable() const { return mItemCheckable; }
 
     /**
      * @brief indexFromLayer returns the model index for a given layer
      */
-    QModelIndex indexFromLayer( QgsMapLayer* layer );
+    QModelIndex indexFromLayer( QgsMapLayer* layer ) const;
 
 
   protected slots:
diff --git a/src/gui/qgsmaplayerproxymodel.cpp b/src/gui/qgsmaplayerproxymodel.cpp
index 8b65482d987..c1c20295404 100644
--- a/src/gui/qgsmaplayerproxymodel.cpp
+++ b/src/gui/qgsmaplayerproxymodel.cpp
@@ -21,9 +21,13 @@
 QgsMapLayerProxyModel::QgsMapLayerProxyModel( QObject *parent )
     : QSortFilterProxyModel( parent )
     , mFilters( All )
-    , mModel( new QgsMapLayerModel( this ) )
+    , mModel( new QgsMapLayerModel( parent ) )
 {
   setSourceModel( mModel );
+  setDynamicSortFilter( true );
+  setSortLocaleAware( true );
+  setFilterCaseSensitivity( Qt::CaseInsensitive );
+  sort( 0 );
 }
 
 QgsMapLayerProxyModel *QgsMapLayerProxyModel::setFilters( Filters filters )
@@ -79,7 +83,7 @@ bool QgsMapLayerProxyModel::filterAcceptsRow( int source_row, const QModelIndex
 bool QgsMapLayerProxyModel::lessThan( const QModelIndex &left, const QModelIndex &right ) const
 {
   // default mode is alphabetical order
-  QString leftId = sourceModel()->data( left ).toString();
-  QString rightId = sourceModel()->data( right ).toString();
-  return QString::localeAwareCompare( leftId, rightId ) < 0;
+  QString leftStr = sourceModel()->data( left ).toString();
+  QString rightStr = sourceModel()->data( right ).toString();
+  return QString::localeAwareCompare( leftStr, rightStr ) < 0;
 }
diff --git a/src/gui/qgsmaplayerproxymodel.h b/src/gui/qgsmaplayerproxymodel.h
index c6dc5747465..13b522a542b 100644
--- a/src/gui/qgsmaplayerproxymodel.h
+++ b/src/gui/qgsmaplayerproxymodel.h
@@ -52,7 +52,7 @@ class GUI_EXPORT QgsMapLayerProxyModel : public QSortFilterProxyModel
     /**
      * @brief layerModel returns the QgsMapLayerModel used in this QSortFilterProxyModel
      */
-    QgsMapLayerModel* sourceLayerModel() { return mModel; }
+    QgsMapLayerModel* sourceLayerModel() const { return mModel; }
 
     /**
      * @brief setFilters set flags that affect how layers are filtered