In general, there is a tradeoff between an orthogonal transform performance and its computational complexity. The Haar transform is by far the fastest of all unitary transforms. The objective of this work is to develop a class of unitary transforms that exhibits computational efficiency as well as good performance utilizing the Haar and slant transforms. This class is called the parametric slant-Haar transforms that includes as special cases the commonly used Haar and slant-Haar transforms. Examples of parametric slant-Haar transforms are given. An efficient fast parametric slant-Haar transform is introduced and its computational complexity is discussed. Relative performance of parametric slant-Haar transforms to that of the Karhunen-Loeve transform (KLT) is discussed. A partially signal dependent parametric slant-Haar transform is also introduced.