[zaarn]

Gravitational slingshots are a method were you accelerate and end up slowing down but I don't think it's fair to say that you "just accelerate to reach a lower orbit", since your acceleration ultimately ends up being either retrograde for very low fly-by orbits or on the normal/radial axis. Or possibly even prograde.

Basically, using a flyby to apply retrograde speed is not much more than accelerating prograde and then using the gravity of a planet to A) move your orbital position without a speed change and/or B) redirect your acceleration.