What quite a few people do in their show tanks (at least some people I know) is place the trimmings back in the substrate so they will grow straight (kinda going off what BruceF said) because the apical meristem is still intact.
The apical meristem, or the main shoot, releases auxin, which is a plant hormone that prevents lower shoots from breaking and sending out new shoots/stems. When the apical meristem is removed, no auxin is being produced/released, which allows for the plant to send out branching shoots. This only occurs if the "apical dominance" is complete i.e. one meristem inhibits the formation of others. If the plant is exhibiting an "incomplete dominance," (only partial inhibition of side shoot formation), then you'll get some side shoots to form.
You could trim off the branched portions of the plant and hope that the plant remains straight, but that doesn't always happen: I always kept getting branching with my ludwigia, so I just let it grow out and become really dense.