  We obtain several estimates for bilinear form with Kloosterman sums. Such
results can be interpreted as a measure of cancellations amongst with
parameters from short intervals. In particular, for certain ranges of
parameters we improve some recent results of Blomer, Fouvry, Kowalski, Michel
and Mili\'cevi\'c and also of Fouvry, Kowalski and Michel. In particular, we
improve the bound on the error term in the asymptotic formula for mixed moments
of $L$-series associated with Hecke eigenforms.
