There is no unique contrast enhancement method, but the existing methods seem to cover all needs for local or global enhancement. Nevertheless, experimental evidence shows that the two main algorithmic classes (histogram based and high pass filter based) have their own characteristic artifacts. This work intends to show that new and simple alternative algorithms in these classes are possible. The two proposed algorithms introduce bounds on the amount of contrast change, permitting to always deliver natural looking enhanced images. Comparison with six state-of the-art methods illustrate the competitiveness of a fast nonlinear local contrast enhancement method by partial differential equation, and of a very simple histogram modification method.