Grey parrots have shown competence equivalent to or better than five-year-old humans in studies on numerical and inferential tasks. I will present the results from research with Alex on numbers and Griffin on inference by exclusion. Demonstrating such competence took many years and multiple experiments. The data not only provide insight into the cognitive capacities of nonhumans who were performing the tasks, but also into that of the humans who were designing the studies: Researchers must constantly be aware of the complexity of the task being studied, and avoid over-interpreting data or thinking that success on a simple task answers a complex question. Researchers must accept the possibility of alternative explanations of the data, design further tasks to rule out these possibilities, and be eager to search for input from colleagues and laboratories with complementary areas of expertise.