We describe a generalization and improvement of Diaz y Diaz's search technique for imaginary quadratic fields with 3-rank at least 2, one of the most successful algorithms for generating many examples with relatively small discriminants, to find quadratic fields with large n-ranks for odd n >= 3. An extensive search using our new algorithm in conjunction with a variety of further practical improvements produced billions of fields with non-trivial p-rank for the primes p = 3, 5, 7, 11 and 13, and a large volume of fields with high p-ranks and unusual class group structures. Our numerical results include a field with 5-rank equal to 4 with the smallest absolute discriminant discovered to date and the first known examples of imaginary quadratic fields with 7-rank equal to 4.