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Images with haze of different varieties often pose a significant challenge to dehazing. Therefore, guidance by estimates of haze parameters related to the variety would be beneficial, and their progressive update jointly with haze reduction will allow effective dehazing. To this end, we propose a multi-network dehazing framework containing novel interdependent dehazing and haze parameter updater networks that operate in a progressive manner. The haze parameters, transmission map and atmospheric light, are first estimated using dedicated convolutional networks that allow color-cast handling. The estimated parameters are then used to guide our dehazing module, where the estimates are progressively updated by novel convolutional networks. The updating takes place jointly with progressive dehazing using a network that invokes inter-step dependencies. The joint progressive updating and dehazing gradually modify the haze parameter values toward achieving effective dehazing. Through different studies, our dehazing framework is shown to be more effective than image-to-image mapping and predefined haze formation model based dehazing. The framework is also found capable of handling a wide variety of hazy conditions wtih different types and amounts of haze and color casts. Our dehazing framework is qualitatively and quantitatively found to outperform the state-of-the-art on synthetic and real-world hazy images of multiple datasets with varied haze conditions.