Many attempts have been made to increase the nutritional value of bread by adding dietary fibre. However, fibre enrichment is usually associated with various technological problems. The aim of this study was to optimise the composition of a blend of inulin, pectin and guar gum to enrich the fibre content of partially baked frozen bread without impairing its technological quality. We prepared 20 formulations following a central composite design, together with 4 control breads. Bread enriched with inulin had higher crumb hardness, lower specific volume, shape, moisture content, and crumb cohesiveness than control bread, but improved flavour. Pectin and guar improved moisture content and crumb cohesiveness. There was no interaction between inulin and pectin for any of the bread attributes investigated, while interactions between inulin and guar were small. In contrast, guar and pectin significantly interacted to decrease volume and increase crumb hardness and chewiness. A desirability function method identified the optimised blend as containing 3% inulin, 0.9–1% pectin and 0.3–0.4% guar. Bread enriched with such blend had the following characteristics: specific volume, 4.06 cm³/g; shape, 0.63; crumb hardness, 189 g; resilience, 0.36; cohesiveness, 0.84; chewiness, 169 g; and flavour score, 4.6. Experimental values were close to the predicted ones, with prediction errors below 10% for all attributes tested. The specific volume, crumb hardness and chewiness of the enriched bread were superior to those of unenriched bread. However, undesirable textural changes occurred in the enriched bread during 12 weeks of frozen storage, and these changes strongly depended on the fibre blend composition