Tight Fitting Drawer - What to do?

Hi, this question may not strictly belong here but I'll ask it.
What do I do about a desk drawer which fits too tightly in the case? I don't want to start pulling off the veneer on the face of the case or damaging the drawer.

Image1 shows the drawer pulled out a bit. In this position it slides easily until Image 2 where the drawer front meets the case.
This is what I've done so far:

• Verified it's the draw sides which are tight and not the top / bottom of the drawer
• Clamped across the front of the drawer to 'pull' the sides closer (no help)
• Waxed the sides of the drawer and the sides of the case (no help)

Before I start 'shaving' the sides of the case I'd like to know how others have fixed these types of problems. As always, thanks for your help!

 

The bottom of the drawer looks like newer wood, possibly a replacement that was not trimmed enough, or has swelled more than the older wood.

 

HA... I was going to suggest that.....because I've done that...... but then thought the furniture guys here would jump me !!

Thank you , Davey !!!!!

 

Possibly a bit of sandpaper on the new wood first.