Random regression analyses have become standard methodology for the analysis of traits with repeated records that are thought of as representing points on a trajectory. Modelling curves as a regression on functions of a continuous covariable, such as time, for each individual, random regression models are readily implemented in standard, linear mixed model analyses. Early applications have made extensive use of regressions on orthogonal polynomials. Recently, spline functions have been considered as an alternative. The use of a particular type of spline function, the so-called B-splines, as basis functions for random regression analyses is outlined, emphasising the local influence of individual observations and low degree of polynomials employed. While such analyses are likely to involve more regression coefficients than polynomial models, it is demonstrated that reduced rank estimation via the leading principal components is feasible and likely to yield more parsimonious models and more stable estimates than full rank analyses. The combined application of B-spline basis function and reduced rank estimation is illustrated for a small set of data for beef cattle.