I purchased the Malm set of 3 drawers (narrow) to use as a bedside table. While I was shopping I also picked up two Billington drawer inserts.
I wanted these inserts to sit at the top of the drawer. The outside lip is wide enough to span the gap of the drawer, but the tapered edges cause the insert to move sideways and drop when placing anything in it.
Step 1: Improving the Fit
The tapered edge is what causes the insert to drop into the drawer.
Tape some cardboard strips to both sides of the insert.
The cardboard should be about half of the width of the gap between the edge of the insert and the tapered side. I used 2 layers of single corrugated cardboard on both sides.
With the right thickness, the insert should give a snug fit when inserted into the drawer.
Step 2: Viola!
The insert now stays in place when putting heavy items in it!
I've been using the inserts for about three weeks and I haven't had to do anything else to them since taping the cardboard in place.