Simple SummaryThe Murciano-Granadina goat is a local breed of importance, not only for the economic and social impact of the breeders but also for its conservation. Estimates of the genetic parameters of peak and persistency traits (not commonly used in breeding schemes) using multivariate models is a feasible tool in early lactation (could genetically modify lactation curves) for improving sustainable production in dairy goats, specifically when more data are available. The genetic variability for the parameters of the lactation curve (peak yield, yield and persistency studied traits) is low. The heritability was low to intermediate in all the traits, being between 0.08 for persistency and 0.17 for yield. The genetic correlations were high for peak yield and yield (0.94), indicating that the selection for both peak production and persistence is feasible, with no detrimental response in either. Murciano-Granadina should be a guide dairy goat, and the result could provide a general strategy applicable to other local breeds.This paper studies parameters of a lactation curve such as peak yield (PY) and persistency (P), which do not conform to the usual selection criteria in the Murciano-Granadina (MG) breed, but are considered to be an alternative to benefit animal welfare without reducing production. Using 315,663 production records (of 122,883 animals) over a period of 24 years (1990–2014), genetic parameters were estimated with uni-, bi- and multivariate analysis using multiple trait derivative free restricted maximum likelihood (MTDFREML). The heritability (h2)/repeatability (re) of PY, yield (Y) and P was estimated as 0.13/0.19, 0.16/0.25 and 0.08/0.09 with the uni-trait and h2 of bi- and multi-traits analysis ranging from 0.16 to 0.17 of Y, while that of PY and Y remained constant. Genetic correlations were high between PY–Y (0.94 ± 0.011) but low between PY–P (–0.16 ± 0.054 to –0.17 ± 0.054) and between Y–P (–0.06 ± 0.058 to –0.05 ± 0.058). Estimates of h2/re were low to intermediate. The selection for Y–PY or both can be implemented given the genetic correlation between these traits. PY–P and Y–P showed low to negligible correlation values indicating that if these traits are implemented in the early stages of evaluation, they would not be to the detriment of PY–Y. The combination of estimated breeding values (EBVs) for all traits would be a good criterion for selection.