Using capacitors to make it faster at the expense of lower input impedance at high frequencies. Just-about handles 3MHz, (depending what output quality you want,) which is 6 times faster than without the capacitors. Input impedance at that speed is something like 7kΩ, maybe less for 10ns or so.
At start, it takes a moment for some capacitors to charge.
Slow but sane version previously published:
http://everycircuit.com/circuit/5498348688900096
Simplification of the circuit which gave me the capacitor idea:
http://everycircuit.com/circuit/5278576218996736
