Wireless sensor network protocols very often use the Trickle algorithm to govern information dissemination. For example, the widely used IPv6 Routing Protocol for Low-Power and Lossy Networks (RPL) uses Trickle to emit control packets. We derive an analytical model of Trickle to take into account multiple redundancy constants and the common lack of synchronization among nodes. Moreover, we demonstrate message count unfairness when Trickle uses a unique global redundancy constant because nodes with less neighbors transmit more often. Consequently, we propose a heuristic algorithm that calculates a redundancy constant for each node as a function of its number of neighbors. Our calculated redundancy constants reduce unfairness among nodes by distributing more equally the number of transmitted messages in the network. Our analytical model is validated by emulations of constrained devices running the Contiki Operating System and its IPv6 networking stack. Furthermore, results very well corroborate the heuristic algorithm improvements.