  Using the measured and projected invisible mass spectrum of the
$K^+\to\pi^+\nu\bar\nu$ mode, we determine the current and future constraints
within the model-independent framework of the weak effective theory at
dimension-six. We work in two different operator bases depending whether
neutrinos are Majorana or Dirac fermions. This makes it possible to
transparently incorporate mass effects of additional sterile neutrinos for all
operators.
