Much of the gameplay in my campaign is centered around exploring the dungeon. Exploring speed is noted on the character sheet, modified by armor and encumbrance. Each ten-minute turn, the party can make a single-, double-, or triple-move.
Single-moves allow you to map the dungeon with more-or-less accurate measurements, and gives 1 in 6 odds for chance encounters. The party is assumed to be watching for unusual features that might indicate a trap, and will have a chance to approach such features cautiously to out-think the trap. If someone in the front rank has a mirror, the players will be given info about what's visible through doorways and around corners while the party still has cover.
Double-moves allow you to consult the map, but you get no measurements while traveling, so any mapping must be sketchy and brief. Chance encounters are checked at 2 in 6 odds, as the party is less stealthy than usual. The party is being less cautious about traps, and has only a 2/6 chance to spot potential trouble before walking into it. Mirrors are being checked only briefly, so that lights and creatures may be spotted while the party has cover, but details will not be immediately obvious.
Triple-moves are the swiftest pace that can be maintained without exhausting the party, being roughly a jog. The party can't consult the map, and check for chance encounters at 3 in 6 odds. Traps can be avoided only by dumb luck (assume a 2/6 chance of each rank passing by unless otherwise noted). Mirrors can't be used effectively, and the party make only 5 triple-moves before it must rest for 1 turn - these moves can be all at once or brief bursts of speed amidst turns of slower travel.