The self-assembly of block copolymers in the bulk phase enables the formation of complex nanostructures with sub 100 nm periodicities and long-range order, both relevant for nanotechnology applications. Here, we map the bulk phase behavior of polystyrene-block-polybutadiene-block-poly(tert-butyl methacrylate) (SBT) triblock terpolymers on a series of narrowly distributed polymers with widely different block volume fractions, ϕS, ϕB and ϕT. In dependence of ϕ, we find the lamella–lamella, core-shell cylinder, cylinder-in-lamella and core-shell gyroid morphology, but also a rarely observed cylinder-in-lamella phase. The bulk morphologies are thoroughly characterized by transmission electron microscopy (TEM) and small angle X-ray scattering (SAXS) and display unusually broad stability regions, i.e. morphologies are observed over a broad range of compositions. We attribute this phase behavior to the asymmetric distribution of block–block incompatibilities, along the SBT block sequence, which are relatively large for S/B and S/T interfaces, but small for B/T. The higher enthalpic penalties at the S/B and S/T interface cause B to preferentially spread on the T microdomain thereby adopting its geometry. The morphological behavior of SBT is thus dominated by the volume ratio of the end blocks, ϕS and ϕT, which reduces the number of potential morphologies to only a few, mostly the core-shell analogue of diblock copolymer morphologies. In general, a simplified terpolymer bulk behavior with large stability regions for morphologies offers straightforward synthetic targeting of specific morphologies that usually only appear in a small parameter space as demonstrated here on the core-shell gyroid.