Deuterium-Deuterium fusion without Tritium is very possible.
Historically, D-D fusion was the first form of nuclear fusion mankind successfully achieved.
It may be worthwhile remembering that, at the dawn of the nuclear age in 1952, an inertial confinement fusion experiment that used nuclear fission to produce the conditions for nuclear fusion called Ivy Mike not only produced net energy (more energy out of the fusion experiment than the energy required to operate the fusion experiment) but achieved a fusion gain factor of Q>=100,000.
Ivy Mike achieved net energy and Q>=100,000 using the D-D fusion reaction.
Note: No other non-military pure fusion experiment in the world has achieved a fusion gain factor Q>1 at any time, even for milliseconds, in the last 60 years.
(Picture of Ivy Mike D-D fusion experiment - 1952)http://www.sonicbomb.com/content/atomic/carc/us/ivy/limg/mikedevice.jpg