I wouldn't necessarily say every battalion was made up of left-over companies. Case in point: The 5th Battalion Miss. Volunteers was an undersized battalion - 3 companies total. They were organized in Mobile around the first of December, 1861. They stayed the same size (same three companies in the battalion) until May 1862 when the battalion was split up by order of Braxton Bragg at Corinth and each company was assigned to a different regiment, one to the 41st MS, one to the 43rd MS and one to the 27th MS. My point being: their organization as a battalion seems intentional and they were not filled out to the size of a regiment.