I think it's fair to say that folks have been grumbling about the rules for pummeling, grappling, and overbearing since the Dungeon Masters Guide was first published. They are, to put it plainly, awful, inelegant, and difficult to use. They don't fit in at all with the rest of the combat system, and the results that they yield often don't make a lick of sense.
Various optional and alternate hand-to-hand rules have been published over the years, some in The Dragon, and yet I've discovered a set of rules that have been lurking under my very nose for almost 30 years. They are quick, can be adapted for use with A/D&D with a minimum of fuss, and make sense in the overall scheme of the combat system.
They are found in TSR's wild west role-playing game Boot Hill, of all places.
Briefly put, here's the system (adapted from pp. 10-11 of the original Boot Hill rulebook, with AD&D-isms inserted as needed).
1. Whoever has the highest dexterity (or initiative, depending on how you play) goes first.
2. You can either punch or grapple.
3. Roll 2d10, add any "to hit" bonus for strength.
4. Consult the Punching Table; that will tell you what sort of punch you were able to do, how much damage you did, and what (if any) "to hit" adjustment your opponent gets next round. Anything over 10 does at least a point of damage; add any strength bonus as applicable.
5. OR, consult the Grappling Table; that will tell you what sort of hold you were able to put on your opponent, how much damage you did, and what sort of "to hit" adjustment you or your opponent gets next round. Anything over 10 does at least a point of damage and puts the opponent in some sort of hold. Next round, the opponent will need to break the hold.
(I've scanned in the tables and the notes that go with them; just click on the image and you should get a full-sized copy.)
And that's pretty much it. I like it because, like most TSR products of the day, it leaves much of the leg-work to the DM; i.e., it requires actual judgement. It will take a little common sense to say, "You got your opponent in a head lock, but he is still able to take a punch at you and hits you in the ribs for 2 points of damage."
Just about the only thing that will need to be taken into account is armor; I'd say if the opponent is wearing a helmet, punching is out. If he's wearing armor, a rabbit punch won't have an effect (if you roll one), but most punches and grappling moves will work (you can still put someone in plate mail into an arm lock). Things like elbow smash are probably out, but again that's for the DM to actually make a decision about. I would toss out the Boot Hill rules for hand weapons completely (essentially, they use the punching table), since A/D&D is built around such things.
I sense a tavern brawl in my players' immediate future.