The present invention is a process for dehydrating an alcohol to prepare corresponding olefin(s), comprising: (a) providing a feed (A) comprising at least an alcohol having at least 2 carbon atoms, and preferably at most 5 carbon atoms, or a mixture thereof optionally water, optionally an inert component, in a dehydration unit, (b) placing the feed (A) into contact with an acidic catalyst in a reaction zone of said dehydration unit at conditions effective to dehydrate at least a portion of the alcohol to make an olefin or a mixture of olefins having the same number of carbon atoms as the alcohol, (c) recovering from said dehydration unit an effluent (B) comprising: an olefin or a mixture of olefins, water, undesired by-products including aldehydes and lighter products resulting from degradation of said aldehydes under the conditions of step (b), optionally unconverted alcohol(s) if any, optionally the inert component, wherein, said feed (A)-providing step (a) comprises adding an effective amount of one or more organic compound capable to reduce the undesired by-products by comparison with a non introduction of such compound, said organic compound being chosen among organic acids.