We develop an efficient Fourier-based numerical method for pricing Bermudan and discretely monitored barrier options under the Heston stochastic volatility model. The two-dimensional pricing problem is dealt with by a combination of a Fourier cosine series expansion, as in [F. Fang and C.W. Oosterlee, SIAM J. Sci. Comput., 31 (2008), pp. 826–848, F. Fang and C. W. Oosterlee, Numer. Math., 114 (2009), pp. 27–62], and high-order quadrature rules in the other dimension. Error analysis and experiments confirm a fast error convergence.