Disclosed are new phosphatidylserine binding constructs with surprising combinations of properties, and a range of diagnostic and therapeutic conjugates thereof. The new constructs effectively bind phosphatidylserine targets in disease and enhance their destruction, and can also specifically deliver attached imaging or therapeutic agents to the disease site. Also disclosed are methods of using the new construct compositions, therapeutic conjugates and combinations thereof in tumor vasculature targeting, cancer diagnosis and treatment, and for treating viral infections and other diseases.