diff --git a/modules/ve/ce/ve.ce.Surface.js b/modules/ve/ce/ve.ce.Surface.js
index d30d197e88..b7d8cb5136 100644
--- a/modules/ve/ce/ve.ce.Surface.js
+++ b/modules/ve/ce/ve.ce.Surface.js
@@ -701,9 +701,7 @@ ve.ce.Surface.prototype.onCopy = function ( e ) {
 	// Clone the elements in the slice
 	slice.data.cloneElements();
 
-	ve.dm.converter.store = slice.getStore();
-	ve.dm.converter.internalList = slice.getInternalList();
-	ve.dm.converter.getDomSubtreeFromData( slice.getData(), this.$pasteTarget[0] );
+	ve.dm.converter.getDomSubtreeFromModel( slice, this.$pasteTarget[0] );
 
 	// Some browsers strip out spans when they match the styling of the
 	// paste target (e.g. plain spans) so we must protect against this
@@ -842,9 +840,13 @@ ve.ce.Surface.prototype.beforePaste = function ( e ) {
 		}
 		context.push( { 'type': '/' + context[0].type } );
 
-		ve.dm.converter.store = doc.getStore();
-		ve.dm.converter.internalList = doc.getInternalList();
-		ve.dm.converter.getDomSubtreeFromData( context, this.$pasteTarget[0] );
+		ve.dm.converter.getDomSubtreeFromModel(
+			new ve.dm.Document(
+				new ve.dm.ElementLinearData( doc.getStore(), context ),
+				doc.getHtmlDocument(), undefined, doc.getInternalList()
+			),
+			this.$pasteTarget[0]
+		);
 
 		// Giving the paste target focus too late can cause problems in FF (!?)
 		// so do it up here.
diff --git a/modules/ve/dm/ve.dm.Converter.js b/modules/ve/dm/ve.dm.Converter.js
index 6f8839b3f3..9a5c222b22 100644
--- a/modules/ve/dm/ve.dm.Converter.js
+++ b/modules/ve/dm/ve.dm.Converter.js
@@ -1072,19 +1072,30 @@ ve.dm.Converter.prototype.isDomAllMetaOrWhitespace = function ( domElements, exc
 ve.dm.Converter.prototype.getDomFromModel = function ( model ) {
 	var doc = ve.createDocumentFromHtml( '' );
 
+	this.getDomSubtreeFromModel( model, doc.body );
+
+	return doc;
+};
+
+/**
+ * Convert document model to an HTML DOM subtree and add it to a container element.
+ *
+ * @method
+ * @param {ve.dm.Document} model Document model
+ * @param {HTMLElement} container DOM element to add the generated elements to. Should be empty.
+ */
+ve.dm.Converter.prototype.getDomSubtreeFromModel = function ( model, container ) {
 	// Set up the converter state
 	this.documentData = model.getFullData();
 	this.store = model.getStore();
 	this.internalList = model.getInternalList();
 
-	this.getDomSubtreeFromData( this.documentData, doc.body, model.getInnerWhitespace() );
+	this.getDomSubtreeFromData( this.documentData, container, model.getInnerWhitespace() );
 
 	// Clear the state
 	this.documentData = null;
 	this.store = null;
 	this.internalList = null;
-
-	return doc;
 };
 
 /**