biochemistry - Protein construct design

I am trying to create some constructs of a certain protein deleting well defined domains (at either terminus) to determine interaction regions with other proteins etc., 3 constructs with varying start/end sites have ended up being aggregated in E coli (while the full length protein expresses reasonably well). My question is what considerations one should use to determine start/end sites to maximize chances of getting soluble, purifiable protein. The criterion I used were:

1. Preferably loop region in known x-ray structure


2. Use hydrophobicity plots to minimize hydrophobic residues at both termini


3. 3-4 residue linker between protein and affinity tag (GST/6xHis)

From personal experience with an earlier construct, this can turn out to be an idiosyncratic exercise but I was wondering if I was missing any crucial parameters.

EDIT: I also played around with the PDB file of the non-truncated protein to check whether huge hydrophobic patches were exposed on deletion of the domain(s), and I didn't find any such patches that could potentially be exposed and lead to aggregation