Despite the major interest in membrane proteins at functional, genomic, and therapeutic levels, their biochemical and structural study remains challenging, as they require, among other things, solubilization in detergent micelles. The complexity of this task derives from the dependence of membrane protein structure on their anisotropic environment, influenced by a delicate balance between many different physicochemical properties. To study such properties in a small protein-detergent complex, we used fluorescence measurements and molecular dynamics (MD) simulations on the transmembrane part of glycophorin A (GpAtm) solubilized in micelles of dihexanoylphosphatidylcholine (DHPC) detergent. Fluorescence measurements show that DHPC has limited ability to solubilize the peptide, while MD provides a possible molecular explanation for this. We observe that the detergent molecules are balanced between two different types of interactions: cohesive interactions between detergent molecules that hold the micelle together, and adhesive interactions with the peptide. While the cohesive interactions are detergent mediated, the adhesion to the peptide depends on the specific interactions between the hydrophobic parts of the detergent and the topography of the peptide dictated by the amino acids. The balance between these two parameters results in a certain frustration of the system and rather slow equilibration. These observations suggest how molecular properties of detergents could influence membrane protein stabilization and solubilization.