Here we present the synthesis and characterization of a new bispidine (3,7-diazabicyclo[3.3.1]nonane) ligand with N-methanephosphonate substituents (L-2). Its physicochemical properties in water, as well as those of the corresponding Cu(II) and Zn(II) complexes, have been evaluated by using UV-visible absorption spectroscopy, potentiometry, H-1 and P-31 NMR, and cyclic voltammetry. Radiolabeling experiments with Cu-64(II) have been carried out, showing excellent radiolabeling properties. Quantitative complexation was achieved within 60 min under stoichiometric conditions, at room temperature and in the nanomolar concentration range. It was also demonstrated that the complexation occurred below pH 2. Properties have been compared to those of the analogue bispidol bearing a N-methanecarboxylate substituent (L-1). Although both systems meet the required criteria to be used as new chelator for Cu-64/67 in terms of the kinetics of formation, thermodynamic stability, selectivity for Cu(II), and kinetic inertness regarding redox- or acid-assisted decomplexation processes, substitution of the carboxylic acid function by the phosphonic moiety is responsible for a significant increase in the thermodynamic stability of the Cu(II) complex (+2 log units for pCu) and also leads to an increase in the radiochemical yields with Cu-64(II) which is quantitative for L-2.