The problem with some of these higher alcohols is that they make azeotropes with water. For example, isobutanol and water form an azeotrope with a boiling point of 89.7 °C.
In a usual ethanol rectifier the top product would be close to the azeotropic ethanol-water mixture (approx 95% ethanol by mass) and the bottom product would be nearly pure water. What this means for the higher alcohols is that at the top of the column their volatility is much less than the ethanol, so they are "pushed" down the column. On the other hand, at the bottom of the column the excess of water results in the higher alcohols forming azeotropes and being "pushed" up the column. The higher alcohols become trapped in the column and small purge streams are taken off just below and just above the feed point to remove them.
In a potable alcohol (i.e. for beverages) plant the common practice is to first distill the alcohol to around 95% to make a crude or industrial grade product, and then use the water scrubbing column mentioned by Muhammad, followed by a redistillation to 95%.
The water column is not really a scrubber. It is often called a wash column or a hydro-selection column. In this column the spirit is diluted down to around 15% with recycled water. This large excess of water allows all the alcohols to form their azeotropes and the increase in volatility of the higher alcohols is greater than the increase in the volatility of the ethanol. The result is that although there is still a large amount of ethanol in the top product, the ratio of the higher alcohols to the ethanol is much higher in the top product than in the feed. This top product is taken to a recovery column where the higher alcohols are taken out as side stream purges as mentioned above.