We show both numerically and experimentally that intense, narrow, and low-divergence beams of light are produced at the apex of dielectric pyramid-shaped microtips. These beams exhibit a Bessel transverse profile but are narrower than the usual Bessel beam, allowing for a significant enhancement of the light intensity inside the beam. They are generated by axicon-like structures with submicrometric height imprinted in glass by combining optical lithography and chemical etching. The resulting beams are experimentally imaged using fluorescence microscopy, in remarkable agreement with numerical computations.