Process for dehydrating an alcohol to prepare corresponding olefin(s), comprising: (a) providing a feed 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 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 comprising: - an olefin or a mixture of olefins, - water, - undesired by-products including aldehydes and light products, comprising H 2, CO, CH 4, - optionally unconverted alcohol(s) if any, - optionally the inert component, wherein, said feed -providing step (a) being further characterized in that an effective amount of one or more compound capable to reduce the undesired by-products by comparison with a non introduction of such compound is added to said feed at step (a) at a weight concentration of at least 0.05 wt % preferably at least 0.1 wt % more preferably at least 0.5 wt % and at most 5 wt% preferably at most 2 wt% and more preferably at most 1 wt% of the total content of said feed with said compound, said compound being chosen among organic acids and wherein said acidic catalyst is at least one compound selected from the group consisting of: A crystalline silicate zeolite having a ratio Si/Al higher than 10, A dealuminated crystalline silicate zeolite, A phosphorous modified zeolite, silica-alumina, alumina, silicated, titanated, zirconated or fluorinated alumina silico-aluminophosphates, a modified crystalline aluminosilicate of the Framework Type FER having Si/Al framework molar ratio greater than 20 and a ratio between strong acid sites and weak acid sites, S/W, lower than 1.0, the ratio S/W being measured by temperature-programmed desorption of ammonia and being determined by the ratio of the peak area of ammonia desorbed above 340°C to that desorbed below 340°C, or any of above cited acidic catalyst, which was subjected to a preliminary pre-coking step and wherein said organic acids refers to organic molecules having acidic properties excluding organic compound having hetero-elements such as alkali metals with the exception of hydrogen, alkaline earth metals, transition metals, or halogens or phosphor, sulphur or nitrogen. (a) providing a feed 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 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 comprising: - an olefin or a mixture of olefins, - water, - undesired by-products including aldehydes and light products, comprising H 2, CO, CH 4, - optionally unconverted alcohol(s) if any, - optionally the inert component, - an olefin or a mixture of olefins, - water, - undesired by-products including aldehydes and light products, comprising H 2, CO, CH 4, - optionally unconverted alcohol(s) if any, - optionally the inert component, A crystalline silicate zeolite having a ratio Si/Al higher than 10, A dealuminated crystalline silicate zeolite, A phosphorous modified zeolite, silica-alumina, alumina, silicated, titanated, zirconated or fluorinated alumina silico-aluminophosphates, a modified crystalline aluminosilicate of the Framework Type FER having Si/Al framework molar ratio greater than 20 and a ratio between strong acid sites and weak acid sites, S/W, lower than 1.0, the ratio S/W being measured by temperature-programmed desorption of ammonia and being determined by the ratio of the peak area of ammonia desorbed above 340°C to that desorbed below 340°C,