Nonaxisymmetric fused-silica microspheres were fabricated by using only one microsphere by virtue of short pulses of a CO2 laser. Highly directional emission from whispering-gallery modes (WGMs) was studied through direct free-space evanescent excitation. The observed quality factors of WGMs are high, up to 2x10(7), despite this deformation. We show that WGMs in slightly deformed microspheres possibly play an important role in cavity quantum electrodynamics research.