These roasts, cut from the rear end of a steer are leaner and a little tougher than loin cuts. A rump roast is cut from the bottom round. If the bone remains, it is a standing rump roast. The top round is a little more tender than the bottom round, but also very lean.
Two ways to improve these cuts are injecting and larding (inserting strips of fat into slits into the roast). Injecting produces a more even distribution of flavor and moisture. Oils or melted butter can be added to the injecting liquid. Look at the AuJus recipes on the Standing Rib Roast page, I use these for beef injections.
I like to inject them and cook indirect using roasting temps around 325° to 375° measured at the grate, then pull them off at 135° or so. They will rise about 5 degrees during the rest.
Slicing thin, against the grain helps keep the meat tender. If in doubt as to the correct direction, sample a slice then change your knife angle and sample again.
If you are cooking this roast specifically for sandwiches (cold subs or hot Italian for example), let the roast rest for 10 minutes, then wrap in foil leaving a gap in the top for venting (and so the foil won't form condensation) and in about an hour, move it to the fridge. The next day when it's chilled it will slice really nicely. You can use some of the AuJus, make a beefy gravy or go as is.
Cooking Time Chart:
2-3/4 pound roast - 325° pit temp - 1.5 hours to reach 135°