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When conducting interferometric tests of freeform optical surfaces, additional optical components, such as computer-generated holograms or deformable mirrors, are often necessary to achieve a null or quasi-null. These additional optical components increase both the cost and the difficulty of interferometric tests of freeform optical surfaces. In this paper, designs using off-axis segments of conics as base surfaces for freeforms are explored. These off-axis conics are more complex base surfaces than typically-used base spheres but remain null-testable. By leveraging off-axis conics in conjunction with additional orthogonal polynomial departures, designs were found with up to an order-of-magnitude of improvement in testability estimates relative to designs that use base spheres. Two design studies, a three-mirror telescope and a wide field-of-view four-mirror telescope, demonstrate the impact of using off-axis conics as the base surface.