The present paper studies an extension of Peng's comparison theorem for backward stochastic differential equations [\textit{S. Peng}, Stochastics Stochastics Rep. 38, No. 2, 119--134 (1992; Zbl 0756.49015)] to backward equations of the following form: \[ dY_t=-f(t,Y_t,Z_t)dt+g(t,Y_t,Z_t)dW_t,\quad t\in[0,T],\;Y_T=\xi\in L^2({\mathcal F}_T^W), \] where \(W\) is the driving Brownian motion. Under suitable conditions on the coefficients \(f,g\) guaranteeing the existence and the uniqueness of the solution \((Y,Z)\) of this equation, the authors compare the solution \(Y\) with the solution \(Y'\) of the equation \[ dY'_t=-f'_tdt+g(t,Y'_t,Z'_t)dW_t,\quad t\in[0,T],\;Y'_T=\xi'\in L^2({\mathcal F}_T^W) \] with a square integrable \(({\mathcal F}_t^W)\)-progressively measurable driver \(f'=f'(\omega,t)\) which does not depend on the solution. It is shown that if \(\xi\leq\) (resp., \(\geq)\xi'\) and \( f(Y',Z')\leq\) (resp., \(\geq)f'\) then also \(Y\leq\) (resp., \(\geq)Y'\). In the case when \(g(t,y,z)=g(t,y)+z\), the Lipschitz assumption on \(f\) is replaced by the weaker one that \(| f(t,y,z)-f(t,y',z)|^2\leq \rho(| y-y'|^2)\) for some concave function \(\rho\) with \(\rho(0)=0,\, \rho(u)>0\) for \(u>0\) and \(\int_{0^+}\rho(u)^{-1}\,du=+\infty\) (this condition is well known from the study of stochastic differential equations; see, e.g., [\textit{N. Ikeda, S. Watanabe}, Stochastic differential equations and diffusion processes. North-Holland Mathematical Library, Vol. 24. Amsterdam--Oxford--New York: North-Holland Publishing Company (1981; Zbl 0495.60005)].