In this evening's 30-minute post-tai chi kung fu class, we learned that you need to hold tightly to your opponent's wrist so they can't get away while you're elbowing them in the face. ELBOW!
Also, if you hold their wrist close to your waist, it's easier to force them to lose their balance (with the application of force to the elbow (ELBOW!)) than if you're holding them away from your body.
Failing to understand this second point initially, I ended up pulling a muscle I didn't know I could pull. It's in a weird place somewhere between my chest and my side. Feels okay now.