  We establish a general large sieve inequality with sparse sets $\mathcal{S}$
of moduli in the Gaussian integers which are in a sense well-distributed in
arithmetic progressions. This extends earlier work of S. Baier on the large
sieve with sparse sets of moduli. We then use this result to obtain large sieve
bounds for the cases when $\mathcal{S}$ consists of squares of Gaussian
integers and of Gaussian primes. Our bound for the case of square moduli
improves a recent result by the authors.
