The total internal reflection lens has been successfully applied to the efficient collimation of light from incandescent lamps and light-emitting diodes, and it is currently being marketed in several retail products. These circularly symmetric designs operated with relatively small sources. Two new forms of the TIR lens have been designed, and prototypes fabricated, for forming beams from fluorescent lamps. The toroidal fluorescent lamp is formed by circularly sweeping a faceted profile about its outer edge. A 5 inch diameter prototype lens has been diamond turned, and has 80% efficiency. When covering a 2.5 inch toroidal source of 0.25 inch minor diameter, it forms a smooth structureless beam of 40 degrees FWHM. The linear TIR lens has a faceted profile that is extended in cylindrical symmetry. In conjunction with a planar back mirror, a 6 inch diameter lens collects 85% of the light from a 5/8 inch lamp. The full width at half maximum is 30 degrees transversely and 120 degrees longitudinally, in a stripe pattern with twin peaks at +/- 47 degrees parallel to the lamp axis. These designs are applicable to other tubular light sources: discharge lamps, such as aircraft strobes and camera flashlamps, as well as neon lamps. They offer greater efficiency, narrower beamwidths, and much more compact profiles than conventional relfector designs.