Membrane proteins usually need to be extracted from their native environment and separated from other membrane components for in-depth in vitro characterization. The use of styrene/maleic acid (SMA) copolymers to solubilize membrane proteins and their surrounding lipids into bilayer nanodiscs is an attractive approach toward this goal. We have recently shown that a diisobutylene/maleic acid (DIBMA) copolymer similarly solubilizes model and cellular membranes but, unlike SMA(3:1), has a mild impact on lipid acyl-chain order and thermotropic phase behavior. Here, we used fluorescence spectroscopy, small-angle X-ray scattering, size-exclusion chromatography, dynamic light scattering, and P-31 nuclear magnetic resonance spectroscopy to examine the self-association of DIBMA and its membrane-solubilization properties against lipids differing in acyl-chain length and saturation. Although DIBMA is less hydrophobic than commonly used SMA(3:1) and SMA(2:1) copolymers, it efficiently formed lipid-bilayer nanodiscs that decreased in size with increasing polymer/lipid ratio while maintaining the overall thickness of the membrane. DIBMA fractions of different molar masses were similarly efficient in solubilizing a saturated lipid. Coulomb screening at elevated ionic strength or reduced charge density on the polymer at low pH enhanced the solubilization efficiency of DIBMA. The free-energy penalty for transferring phospholipids from vesicular bilayers into nanodiscs became more unfavorable with increasing acyl-chain length and unsaturation. Altogether, these findings provide a rational framework for using DIBMA in membrane-protein research by shedding light on the effects of polymer and lipid properties as well as experimental conditions on membrane solubilization.