The analysis of behavioural organisation can improve the lives' of animals used in research through study of the Rules that determine behaviour, the Relations between animals and the use of Robotics to study behaviour using simulations. The National Centre for the Refinement, Replacement and Reduction (NC3Rs) is a UK initiative to improve the welfare of research animals. Here we show how our three analytical Rs map onto the NC3Rs, using examples from our research. Firstly, we demonstrate how rules-based approaches can refine research by improving understanding of animal welfare and research validity. This is illustrated by research conducted on the repetitive behaviour of caged European starlings (Sturnus vulgaris) using Markovian and semi- Markovian methods. We found that a semi- Markovian method correlated with counts of stereotypic somersaulting behaviour (Kendall's t = 0.635, p= 0.043). Secondly, we demonstrate analysis of social relations, using an example in laying hens. Hens kept in small groups were found to become more clustered over a six week period, spending more time in patches which contained other hens (GLMM: F 1, 28 = 154.66, p = 0.029). Consideration of social behaviour can provide refinement by encouraging appropriate group-housing for animals. It can also offer statistical treatment that maximizes use of behavioural data in group-housed animals, resulting in a need for fewer animals. Finally, we demonstrate how robotics in the form of computational modelling can accelerate experimental findings. The model we present distinguishes between the contributions of social and resource attraction in determining the movements of laying hens. To some degree models can replace the use of live animals and can reduce the number of animals required. Continued application of simulations to the field of animal welfare will also contribute to refinements in the way animals are housed.