Ooohhh... Tall order. Pairing a "mild" cigar against something like a Havana Club Barrel Proof rum. Especially if you're saying Cohiba and Punch is "too harsh".

Have you tried a Montecristo #2? I know it's not exactly mild, but is an excellent pairing with something like Havana Club Barrel Proof. I've always appreciated Montecristo's woodiness paired with the more full flavored and spiciness of something like a barrel proof spirit. You don't seem lose either the cigar or the spirit in pairing.

...and I suppose it depends on which Cohiba vitola you're smoking. If you did not like a Cohiba Robusto, you might want to try the Lancero (or vice versa). That could make all the difference in the world.

The other thing to consider with Cuban cigars is age. Oftentimes "younger" Cuban cigars smoke more raw and harsh than the same cigar that's rested for several years. I once smoked a Quintero Brevas that was most memorable. It had aged for several years. Most pleasant and flavorful, but not in the least bit harsh or raw.

BTW - since you're on the right side of the "pond", have you been dabbling in that most incredible elixir those Scotsmen have been brewing? If I were in your neighborhood there'd be no stopping me heading to the distilleries! LOL

Cheers!

Cheers!