We present a hybrid approach to bounding exponential sums over $k$th powers via Vinogradov's mean value theorem, and derive estimates of utility for exponents $k$ of intermediate size.
"On Weyl sums for smaller exponents." Funct. Approx. Comment. Math. 46 (1) 91 - 107, March 2012. https://doi.org/10.7169/facm/2012.46.1.7