Techniques are described for updating a value of a Rice parameter used to define Golomb codes for coefficient level coding. The Golomb codes defined by the Rice parameter may be used to code a remaining absolute value of a coefficient level for at least one coefficient in a coefficient group (CG). According to the techniques, the value of the Rice parameter is updated based on a selection of a minimum of either a maximum value of the Rice parameter or a variable increment of the value of the Rice parameter. The variable increment is determined based on the value of the Rice parameter and an absolute value of the coefficient level for the current coefficient being coded. Techniques are also described for adjusting the value of the Rice parameter used to define Golomb codes for coefficient level coding based on whether a transform is applied to a transform block.