In one of the answers to this question about the Concorde's lack of high-lift devices on its wings, it was pointed out that the Concorde, using a tailless delta wing, wouldn't have been able to use flaps, since there was no horizontal tail aft of the wing to counteract the downward pitching moment that would result from deploying flaps.
On the other hand, a tailed-delta configuration (a delta wing with a conventional tail mounted aft of the wing) would have been able to use flaps, as it would have had a separate elevator further aft with the ability to counteract the flap-generated pitching moment. A good example of this would be the design for the Boeing 2707-300, which was to use a tailled-delta configuration and would have had some rather impressive flaps, but was cancelled in 1971 before even the two prototypes had been completed.
Given that it would have allowed the inclusion of flaps, would a tailed-delta configuration have been a better choice for the Concorde than the tailless delta they ultimately went with?
Edit: Better in that it would have greatly increased the Concorde's subsonic efficiency and allowed lower-speed (and thus less potentially-tyre-explodey*) takeoffs.
Quoth the linked question:
...The lack of high-lift devices considerably reduced lift at low speeds, requiring the Concorde to take off and land at higher speeds and angles of attack than if it had been equipped with flaps and slats. As well as greatly increasing drag (and thus fuel consumption) during takeoff and landing, this greatly increased the force carried by the main landing gear and the speed at which its tyres had to spin; as a result, if and when a tyre blew out (due to, for instance, a piece of debris left by the previous airplane to use the runway), the results would be much worse than with a tyre blowout on a subsonic airliner.
...[The addition of high-lift devices], along with slightly larger wings and more powerful engines, would have allowed the Concorde B to dispense with afterburners, considerably increasing its fuel efficiency and range.
* It happened a lot before the fatal accident.