We are interested in various constructions of Ritt operators, specifically addressing the question of whether an operator whose spectrum is contained in a Stolz domain of \(\overline {\mathbb {D}}\) is automatically a Ritt operator. We show that this holds true for several natural classes of multiplication operators but we also provide a sharp counter-example. For operators acting on Hilbert space, we show that having the numerical range included in a Stolz domain is sufficient to be a Ritt operator and moreover, we construct classes of operators with this numerical range property. Further, we show that any interpolated operator between a power bounded operator and a Ritt operator is still a Ritt operator, which is a fundamental result for the study of diffusion operators.