I myself am thoroughly pleased with Magic: the Gathering's solution for this. Floor rules say you can pile shuffle at first if you want to. Pile shuffling, as I mean it, is drawing the top card of the deck, putting it into one pile, then taking the second card and putting it into the second pile, then taking the third card and putting it into a third pile, then putting the fourth back in the first pile, lather, rinse repeat. You don't have to use 3, I usually used 6. After you're done, you put pile one on top, pile three on bottom and pile two in the middle.
Pile shuffling is not shuffling, it doesn't randomize the cards. It deliberately weaves the cards in your deck throughout your deck in an even consistency. So I pile shuffle my deck before I get to the tournament table or first thing when I get there. And I know I'm holding a beastly stacked deck now.
Then, each player has to actually randomize their deck in front of eachother. So I take the deck I've stacked and riffle shuffle and overhand it. I'm ruining the deck. I'm a little bit OCD about it so I usually keep shuffling it until it "feels good", but if I wanted to win badly I could try to shuffle it as little as my opponent would allow.
Then after the public shuffling, your opponent has the last chance to shuffle your deck as much. Not just cut, but shuffle (which might have been a recent development around the time I started), cutting won't undo a weave.
Your opponent is the last person to touch your deck. Once he's done shuffling and cutting it (he's not allowed to look at it, so he is unable to sabotage your deck), you draw whatever card is on top and go. Most of the time, he sees that you randomized your deck with enough riffle shuffling and simply cuts.
The system always struck me as being fair in a kind of "I'll cut the cookie, you choose which half" kind of way. The last line of defense is your opponent ensuring your deck is randomized, and if he fails at that duty, you get a strong deck. If you're worried about an opponent getting good draws, just shuffle his deck well.
Dominion has lots of shuffling of course, but I empathize with the players that want to order their discard pile, then randomize from there. I'd suggest letting your friends do so and having the player to their left perform their shuffles.