This paper introduces variants of strangles, called Euro-American or hybrid strangles, and it promotes a new numerical pricing technique. We highlight and compare the properties of European, American, and hybrid strangles with pricing and hedging in mind. The new quadrature approach we propose can account for systems of coupled integral equations that locate the early exercise boundaries of finite-lived contracts. We show that this method is efficient, accurate, and fast for pricing all types of early exercisable strangles. Other advantages of this technique are that it avoids the non-monotonic gradient problem faced by others and it allows users to control for errors. We then investigate the hedging of all strangles, we derive analytical expressions for some Greek parameters, and we stress how these parameters can differ (or not) from each other.