Efficient sources of individual pairs of entangled photons are required for quantum networks to operate using fiber-optic infrastructure. Entangled light can be generated by quantum dots (QDs) with naturally small fine-structure splitting (FSS) between exciton eigenstates. Moreover, QDs can be engineered to emit at standard telecom wavelengths. To achieve sufficient signal intensity for applications, QDs have been incorporated into one-dimensional optical microcavities. However, combining these properties in a single device has so far proved elusive. Here, we introduce a growth strategy to realize QDs with small FSS in the conventional telecom band, and within an optical cavity. Our approach employs ‘‘droplet-epitaxy’’ of InAs quantum dots on (001) substrates. We show the scheme improves the symmetry of the dots by 72%. Furthermore, our technique is universal, and produces low FSS QDs by molecular beam epitaxy on GaAs emitting at ∼900 nm, and metal-organic vapor-phase epitaxy on InP emitting at ∼1550 nm, with mean FSS 4× smaller than for Stranski-Krastanow QDs.