I just posted a long list of data from Parker & Dubberstein's Babylonian Chronology and The Cambridge Ancient History over in the K.I.S.S. thread:
http://www.jehovahs-witness.com/10/55372/1.ashx
Scholar,
There are dated cuneiform tablets for each year of each neo-Babylonian king. By looking at the last dated tablet for each king and observing the time which elapsed between that tablet and the first tablet dated to his successor, it is easy to see that the chain is unbroken.
Furthermore, the WTS agrees with those regnal lengths in the 1965 article I have cited several times previously.
If you start with the WT's own date of 539 and count backwards through the kings as they are listed in the 1965 WT article, you will arrive at 586/7 for the destruction of Jerusalem.
The unbroken chain of dated cuneiform tablets shows that there were no other kings, and it also shows that none of the kings reigned longer than the time stated in the 1965 WT article.
See the other thread for full information.
Marjorie