An extensive study has been made of the magnetic properties of LaMnO3+delta with finely tuned hole concentrations, x (=2 delta), ranging between 0.08 and 0.15. As x increases in the range studied, the spontaneous magnetisation at low temperature increases from only about 20% to almost 100% of the value for full polarisation of Mn spins, and the coercivity H-c decreases by more than an order of magnitude, e.g. from 4.2 kOe to 120 Oe at 5 K. The magnetic ordering temperature T-c takes a minimum at x = x(c) similar to 0.12 For x <x(c), the inverse susceptibility shows a marked decrease as: T-c is approached from above. Measurements of minor hysteresis loops for the sample with x = 0.08 show that magnetisation is reversible with respect to field changes except near H-c. These observations are discussed in terms of a two-phase exchange coupling (TPEC) model in which it is assumed that at low temperature the system separates into two phases, a hole-free antiferromagnetic phase and an optimally doped ferromagnetic phase, and the two phases are coupled through superexchange interactions at the interface.