A process for oligomerizing isoolefins, the process including: feeding an isoolefin to an oligomerization reaction zone; feeding an oxygen-containing reaction moderator to the oligomerization reaction zone; concurrently in the oligomerization reaction zone: contacting the isoolefin with an oligomerization catalyst to convert at least a portion of the isoolefin to oligomers comprising dimers and trimers of the isoolefin; reacting a portion of the moderator with a portion of at least one of the isoolefin and the oligomers to form an oxygenated oligomerization byproduct; recovering an effluent from the oligomerization reaction zone comprising the oligomers and the oxygenated oligomerization byproduct; fractionating at least a portion of the effluent to recover a fraction comprising the oxygenated oligomerization byproduct and the trimers and a fraction comprising the dimers.