This is a 2-state fit using Paul's priors:

E0=2+/- 2, delta E = 0.4 +/- 0.2, Zn^2 = 10 +/- 10

E0: 1.977973 +- 0.007807
E1: 2.358272 +- 0.183531
ln(Z0): 0.979710 +- 0.026830
ln(Z1): -0.626092 +- 1.017405
chi^2/dof = 9.929 / 15 = 0.662 (0.121 from Bayes priors)