  We consider stochastic differential equations (SDEs) driven by small L\'evy
noise with some unknown parameters, and propose a new type of least squares
estimators based on discrete samples from the SDEs. To approximate the
increments of a process from the SDEs, we shall use not the usual Euler method,
but the Adams method, that is, a well-known numerical approximation of the
solution to the ordinary differential equation appearing in the limit of the
SDE. We show the consistency of the proposed estimators as well as the
asymptotic distribution in a suitable observation scheme. We also show that our
estimators can be better than the usual LSE based on the Euler method in the
finite sample performance.
