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Fluctuations in the cosmic microwave background (CMB), the radiation left over from the Big Bang, contain information which has been pivotal in establishing the current cosmological model. CMB data can also be used to test theoretically well-motivated additions to the model, including pre-inflationary relics (signatures of bubble collisions arising in eternal inflation) and topological defects that form after inflation (cosmic strings and textures). These relics typically leave sub-dominant, spatially localised signals, hidden in the “noise” of the primary CMB, the instrumental noise, foreground residuals and other systematics. Standard approaches for searching for such signals involve focusing on statistical anomalies, which carry the danger of extreme a posteriori biases. The self-consistent approach to this problem is Bayesian model comparison; however, the full implementation of this approach is computationally intractable with current CMB datasets, and will only become more difficult with data from the next generation of CMB experiments. I will describe a powerful modular algorithm, capable of coping with the volume of data, which combines a candidate-detection stage (using wavelets or optimal filters) with a full Bayesian parameter-estimation and model-selection stage performed in pixel space within the candidate regions. The algorithm is designed to fully account for the “look-elsewhere” effect, and its use of blind analysis techniques further enhances its robustness to unknown systematics. Finally, I will present the results of applying the algorithm to hunt for the signatures of bubble collisions and cosmic textures in the seven-year data from the Wilkinson Microwave Anisotropy Probe.