A controlled stochastic integral equation governed by a standard Wiener process and a Poisson measure is considered. The author is looking for an \(\varepsilon\)-optimal admissible control \(\eta_{\varepsilon}\), \(J(\eta_{\varepsilon})<\inf \{J(\eta)\), \(\eta\in {\mathcal U}\}+\varepsilon\) where the admissible class of controls \(\mathcal U\) contains functionals \(\eta: [0,T]\times\mathcal D_ T\to\mathbb R^ d\) which are piecewise constant with respect to \(t\in [0,T]\), where \({\mathcal D}_ T\) is the space of cadlag functions. Three theorems are stated and the last one asserts the existence of an \(\varepsilon\)-optimal control having the above particular structure.