<p>A key premise driving the problem of unconceived alternatives is that contemporary scientists are no better than their predecessors at envisioning serious rivals to even the most well-confirmed scientific theories. Some realists reject this, arguing that present-day science is capable of more severe tests and more comprehensive searches of the space of theoretical alternatives than were previously possible. One way to support this response appeals to the fact that much contemporary science is computational, facilitated by large-scale digital computers. However, we argue that advanced computational tools and methods often impose a tradeoff between generating high-resolution predictions and performing lower-resolution scans of possibility space, which may exacerbate rather than attenuate concerns about unconceived alternatives. We illustrate by considering a specific, highly computational branch of contemporary science: gravitational-wave astronomy.</p>