A detailed model of AlxGa1-xAs double-heterojunction bipolar transistors is used to examine the effects on the cut-off frequency of varying both the degree of base grading in abrupt-junction devices, and the amount of base-collector junction grading in uniform-base devices. It is shown that, in the graded-base case, there is an optimum degree of base grading, stemming from the trade-off between the strength of the aiding field for minority carrier transport across the base and the height of the barrier at the base-collector junction, which inhibits charge flow to the collector. In the uniform-base case, it is shown that a small amount of base-collector junction grading is sufficient to effectively remove the blocking action of the conduction band discontinuity, and so allow the base transit time to attain its diffusion-limited value.