The steady-state performance of a parametrically or structurally uncertain system can be optimized using iterative real-time optimization methods such as modifier adaptation. Here, we extend a recently proposed second-order modifier-adaptation scheme in two important directions. First, we accelerate its convergence, that is, we reduce the number of potentially time-consuming and suboptimal transitions to intermediate steady states by appropriate filtering. Second, we propose an adaptation strategy to reduce conservatism and prevent divergence that could arise from the unknown curvature of the steady-state system performance. Moreover, we combine these two innovations in the unconstrained and convex case and propose a modified acceleration mechanism for constrained and nonconvex problems. Finally, we demonstrate the benefits on two numerical examples. (C) 2018 Elsevier Ltd. All rights reserved.