We introduce a new class of variable kernels which depend on the smoot
hing parameter b through a simple scaling operation, and which have go
od integrated mean square error (IMSE) convergence properties. These k
ernels deform ''automatically'' near the boundary, eliminating boundar
y bias. Computational formulas are given for all orders of kernel in t
erms of exponentially damped sines and cosines. The kernel is a comput
ationally convenient approximation to a certain Green's function, with
the resulting kernel estimate closely related to a smoothing spline e
stimate.