1. A method for applying a content defined minimum size bound on content defined segmentation of data into blocks using a processor device in a computing environment, comprising: defining a plurality of segmenting probabilities and a plurality of segmenting conditions, wherein each of the plurality of segmenting conditions is associated with one of the plurality of segmenting probabilities; ordering the plurality of segmenting conditions in accordance with the associated one of the plurality of segmenting probabilities to form a hierarchy of the plurality of segmenting conditions; defining a segmenting condition associated with a highest segmenting probability to be a lowest level segmenting condition in the hierarchy of the plurality of segmenting conditions, and defining the segmenting condition associated with a lowest segmenting probability to be a highest level segmenting condition in the hierarchy of the plurality of segmenting conditions; defining a minimum bound on a size of a block; calculating a plurality of hash values for each seed block in each consecutive byte position in the data; evaluating each one of the plurality of hash values using the plurality of segmenting conditions; determining a position of one of the plurality of hash values as a candidate segmenting position in the data if at least one of the plurality of segmenting conditions is satisfied by the hash value; defining a hierarchy level of a candidate segmenting position as the hierarchy level of the highest level segmenting condition that is satisfied by the one of the plurality of hash values of the candidate segmenting position; calculating the size of the interval of data between a newly found candidate segmenting position and a previous candidate segmenting position; and discarding the newly found candidate segmenting position if the size of the interval of data is lower than the minimum bound on the size of a block.