10 minutes? that's a short fight around these parts
I must admit, it's difficult keeping people focused, and keeping the game moving. Preparation helps a lot. So, a few questions:
Firstly, which edition of D&D are you using? I much prefer 3.5 myself, but 4th ed is apparently quicker for combats. If you're only using combat occasionally, perhaps move over to 4th ed, to keep things streamlined?
Secondly, do you use models in your game, or do you just use narrative story telling? Fights can be a lot easier if you have a map ready, and use models. If you or a friend have a Warhammer Fantasy empire army, you'll have a lot of human warriors to use. If you have a friend with and Ork and goblin army, you've got some nice savage enemies you can use. Having the visuals can really help, and you can simply use a different model to denote who is the captain of the guard, the Ork Chief or whatever. It gives the players something to focus on, so when you say something, they'll have something to refer to. If you're just using narrative, you'll find players that drift off (and they always do) can't remember what he's doing, or lose track of how many enemies they're fighting.
Thirdly, what do you usually send against them? I find a horde of easy to kill thing, with one or two tougher commanders works well. People like to be effective in combat, so if they're just spending 3-4 turns just doing 5 damage, it's boring. Things the average party member can kill in 1-2 rounds work well, then have the leader/boss for doing interesting things. When even your weaker characters are making the occasional kill, it makes them part of the action too, and you're combat characters can focus on taking down the leaders.
Alternatively, send them up against a single big thing, where they really have to work in concert to take it down. Something they have to really work out a plan to take it down, and then let them figure it out, propose it, and finally carry it out. To keep that part moving, I suggest having an egg timer or something "work out what your doing, and if it's not done when the timer runs out, you're frozen in shock and doing nothing".
My last piece of advice would be to keep things moving, and keep them simple. In your example with the bar fight, rather than rolling for the guy to hide under the table, and then for the guards to see him, just let him hide. A guard in a bar fight wouldn't be looking for people cowering under tables, when there are far more obvious targets around - if he started stabbing/shooting people, and ducking back into cover, then they'd go looking for him. Only roll hide when someone is looking for them, only roll move silently when someone is listening. Less dice rolls are better, think about any way you can take them out of the equation.
I have house rules about Criticals and Critical misses - when you roll them, I choose what they do. When someone rolls a 20, I'll narrate how they just did some amazing feat of swordsmanship/archery/whatever, and have it pretty much kill any non-boss creature. For instance, in the last mission I DM'd (a lvl. 2 adventure), goblins were raiding the house the PCs were in. A Rogue with a crossbow, hidden in the rafters, rolled a 20 against a goblin Jumping in through the window. Rather than rolling crits, and making him roll a little extra damage, I just described how the bolt had pieced through his neck, and thrown the little goblin back towards the window, tangling up a second goblin who was just coming in. This made the Rogue feel extremely effective, and allowed a nearby beguiler to savagely beat the second goblin with an iron bound book. So using this sort of thing, bring the narrative into the fight, make those rolls count.
Other ways to streamline - always have your enemies statlines ready to go, and use the same amount of health for them. Don't have random HP or abilities, and if they have a selection of spells, just choose one or two useful ones, and just make up the rest - you don't have to obey the rules for them
Hope that helps somewhat