Abstract A technique is proposed for smoothing a broken line fit, with known break points, to observational data. It will be referred to as ‘broken line smoothing’. The smoothness term is defined by means of the angles formed by the consecutive segments of the broken line, and is given an adjustable weight. The roughness of the resulting broken line can then be controlled by appropriately tuning the weight of smoothness term and the number of straight-line segments. The broken line smoothing can be used for data analysis in several applications as an alternative to other methods such as locally weighted regression and smoothing splines. The mathematical background and details of the method as well as practical aspects of its application are presented and discussed. Also, several examples using both synthesised and real world (hydrological and climatological) data are presented to explore and illustrate the methodology.