Shallow water tables protect northern peatlands and their important carbon stocks from aerobic decomposition. Hydraulic conductivity, K, is a key control on water tables. The controls on K, particularly in degraded and restored peatlands, remain a subject of ongoing research. We took 29 shallow (~50 cm) peat cores from an estuarine raised bog in Wales, UK. Parts of the bog are in close-to-natural condition, while other areas have undergone shallow peat cutting for fuel and drainage, followed by restoration through ditch blocking. In the laboratory we measured horizontal (Kh) and vertical (Kv) hydraulic conductivity. We fitted linear multiple regression models to describe log10-transformed Kh and Kv on the basis of simple, easy-to-measure predictors. Dry bulk density and degree of decomposition were the strongest predictors of Kh and Kv. Perhaps surprisingly, the independent effect of hummocks was to produce higher-Kv peat than in lawns; while the independent effect of restored diggings was to produce higher-K peat than in uncut locations. Our models offer high explanatory power for Kh (adjusted r2 = 0.740) and K (adjusted r2 = 0.787). Our findings indicate that generalizable predictive models of peat K, similar to pedotransfer functions for mineral soils, may be attainable. Kh and Kv possess subtly different controls that are consistent with the contrasting roles of these two properties in peatland water budgets. Our near-surface samples show no evidence for the low-K marginal peat previously observed in deeper layers at the same site, indicating that such structures may be less important than previously believed.