diff --git a/src/Cursor.cpp b/src/Cursor.cpp
index 911331861d..b427f8cbed 100644
--- a/src/Cursor.cpp
+++ b/src/Cursor.cpp
@@ -322,6 +322,15 @@ void Cursor::dispatch(FuncRequest const & cmd0)
 	// object will be used again.
 	if (!disp_.dispatched()) {
 		LYXERR(Debug::DEBUG, "RESTORING OLD CURSOR!");
+		// We might have invalidated the cursor when removing an empty
+		// paragraph while the cursor could not be moved out the inset
+		// while we initially thought we could. This might happen when
+		// a multiline inset becomes an inline inset when the second 
+		// paragraph is removed.
+		if (safe.pit() > safe.lastpit()) {
+			safe.pit() = safe.lastpit();
+			safe.pos() = safe.lastpos();
+		}
 		operator=(safe);
 		disp_.update(Update::None);
 		disp_.dispatched(false);
@@ -1790,9 +1799,35 @@ bool Cursor::upDownInText(bool up, bool & updateNeeded)
 		row = pm.pos2row(pos() - 1);
 	else
 		row = pm.pos2row(pos());
-		
-	if (atFirstOrLastRow(up))
+
+	if (atFirstOrLastRow(up)) {
+		// Is there a place for the cursor to go ? If yes, we
+		// can execute the DEPM, otherwise we should keep the
+		// paragraph to host the cursor.
+		Cursor dummy = *this;
+		bool valid_destination = false;
+		for(; dummy.depth(); dummy.pop())
+			if (!dummy.atFirstOrLastRow(up)) {
+				valid_destination = true;
+				break;
+			}
+
+		// will a next dispatch follow and if there is a new 
+		// dispatch will it move the cursor out ?
+		if (depth() > 1 && valid_destination) {
+			// The cursor hasn't changed yet. This happens when
+			// you e.g. move out of an inset. And to give the 
+			// DEPM the possibility of doing something we must
+			// provide it with two different cursors. (Lgb, vfr)
+			dummy = *this;
+			dummy.pos() = dummy.pos() == 0 ? dummy.lastpos() : 0;
+			dummy.pit() = dummy.pit() == 0 ? dummy.lastpit() : 0;
+
+			updateNeeded |= bv().checkDepm(dummy, *this);
+			updateTextTargetOffset();
+		}	
 		return false;
+	}
 
 	// with and without selection are handled differently
 	if (!selection()) {
diff --git a/src/Text3.cpp b/src/Text3.cpp
index 4d861f83a4..721355ba94 100644
--- a/src/Text3.cpp
+++ b/src/Text3.cpp
@@ -569,6 +569,19 @@ void Text::dispatch(Cursor & cur, FuncRequest & cmd)
 				&& cur.boundary() == oldBoundary) {
 			cur.undispatched();
 			cmd = FuncRequest(LFUN_FINISHED_FORWARD);
+		
+			// we will probably be moving out the inset, so we should execute
+			// the depm-mechanism, but only when the cursor has a place to 
+			// go outside this inset, i.e. in a slice above.
+			if (cur.depth() > 1 && cur.pos() == cur.lastpos() 
+				  && cur.pit() == cur.lastpit()) {
+				// The cursor hasn't changed yet. To give the 
+				// DEPM the possibility of doing something we must
+				// provide it with two different cursors.
+				Cursor dummy = cur;
+				dummy.pos() = dummy.pit() = 0;
+				cur.bv().checkDepm(dummy, cur);
+			}
 		}
 		break;
 
@@ -582,6 +595,19 @@ void Text::dispatch(Cursor & cur, FuncRequest & cmd)
 			&& cur.boundary() == oldBoundary) {
 			cur.undispatched();
 			cmd = FuncRequest(LFUN_FINISHED_BACKWARD);
+
+			// we will probably be moving out the inset, so we should execute
+			// the depm-mechanism, but only when the cursor has a place to 
+			// go outside this inset, i.e. in a slice above.
+			if (cur.depth() > 1 && cur.pos() == 0 && cur.pit() == 0) {
+				// The cursor hasn't changed yet. To give the 
+				// DEPM the possibility of doing something we must
+				// provide it with two different cursors.
+				Cursor dummy = cur;
+				dummy.pos() = cur.lastpos();
+				dummy.pit() = cur.lastpit();
+				cur.bv().checkDepm(dummy, cur);
+			}
 		}
 		break;
 
diff --git a/status.16x b/status.16x
index d01badb771..cd0987362f 100644
--- a/status.16x
+++ b/status.16x
@@ -211,6 +211,8 @@ What's new
 - Do not open files during startup that were closed in the previous
   session by Close View or Close Window (bug 5458).
 
+- Remove empty paragraphs and superfluous spaces when leaving an inset
+  (bug 5435).
 
 * DOCUMENTATION AND LOCALIZATION