This paper presents the necessary conditions to ensure a minimal profitability of carrier-led consolidation strategies in urban distribution. These conditions are shown by compact formulas obtained by continuous approximations representing the cost of the stakeholders involved: society, regular carriers, consolidation facility operator and environment. The domain of the retailer density variable that always produces negative effects on each stakeholder has been identified. The envelope of this domain does not depend on vehicle costs and other site-related parameters. On the other hand, there is a critical density of receivers that makes the carrier cost savings higher than the CF operator costs.