  We examine the Newman-Janis algorithm's application to an exact regular
static solution sustained by a minimally coupled scalar field with a
non-standard kinetic term. Although coordinate complexification leads to a
regular Kerr-like black hole, we are facing discrepancies in Einstein's
equations in a fairly small domain, for which the regularizing parameter is
responsible. Outside this most intriguing region, the geometry is nothing but
the standard Kerr spacetime.
