We report the coupling of individual InAs quantum dots (QDs) to an external-mirror microcavity. The external mirror is bonded to a fiber and positioned above a semiconductor sample consisting of a QD-containing GaAs layer on top of a distributed Bragg reflector. This open cavity can be rapidly tuned with a piezo-electric actuator without negatively affecting the QD linewidth. A mirror radius of curvature of 42 mu m and a cavity length of 10 mu m enable good mode matching and thus high collection efficiency directly into the fiber. With an improved finesse, this system may enter the strong coupling regime. (C) 2009 American Institute of Physics. [doi:10.1063/1.3245311]