  We consider a minimalist model for the Sterile Insect Technique (SIT),
assuming that residual fertility can occur in the sterile male
population.Taking into account that we are able to get regular measurements
from the biological system along the control duration, such as the size of the
wild insect population, we study different control strategies that involve
either continuous or periodic impulsive releases. We show that a combination of
open-loop control with constant large releases and closed-loop nonlinear
control, i.e. when releases are adjusted according to the wild population size
estimates, leads to the best strategy in terms both of number of releases and
total quantity of sterile males to be released.Last but not least, we show that
SIT can be successful only if the residual fertility is less than a threshold
value that depends on the wild population biological parameters. However, even
for small values, the residual fertility induces the use of such large releases
that SIT alone is not always reasonable from a practical point of view and thus
requires to be combined with other control tools. We provide applications
against a mosquito species, \textit{Aedes albopictus}, and a fruit fly,
\textit{Bactrocera dorsalis}, and discuss the possibility of using SIT when
residual fertility, among the sterile males, can occur.
