Dear  Huabin,

 I could share some experience we had with a larger dataset of thin filaments. When starting, we were not sure about the helical parameters because of resolution limit, tilting of the filaments, heterogeneity etc. We indexed the total power spectrum (or a subset after classification) into different possibilities and tested the convergence of the data around each possibility and selected the particles converged around the indexed solutions.  I followed what Dr. David DeRosier's lecture notes for indexing. Because the indexing only gives a rough estimate,  the converged solutions may deviate for the selection rules. Because the search usually is based on a least-squares type scheme, we used convergence from four diagonal positions, +/1 (1-2) degrees away from the converged rotation angle and +/1 (0.5 to 1.0 A) away from the converged rise,  to select the “right” possibility (ies) and discard particles before refining the parameters further. However, one may argue that the radii of convergency may be so narrow that we might lose some “correct" possibilities. Moreover, the convergency test may not be rigorously smooth because of local minima or we are searching for a better local minima. The counter-argument is that the helical property is a macroscopic feature, and does not need atomic resolution to reach good registration among particles if they are really in the same symmetry group. To this point, Dr. Egelman’s earlier JSB papers demonstrated robust convergency as a convincing feature. Further, I heard from multiple others that the helical filaments may be intrinsically heterogeneous and sensitive to changes in experimental conditions because of the repetitive interactions at interfaces. Given this point, the physiological relevancy of the data and the resulted model(s) would need to be tested from many angles. 

I hope that these do not make it very complex. In your case, the two searches did not converge from the two initial positions. More tests around the indexed solutions might hep.  As others suggested, verification with all possible ways would be preferred. If you have a lot more data and can classify them into different subgroups for indexing, it may be better. 

Best luck,

Qiu-Xing