Jesse Tree Madness!
Now, you may ask yourself (or more likely, your kids may ask you) why Jesse Trees don't include all of Jesus' ancestors on them.
Without even getting into Levirate marriages and dual sonship, this is why.
For my money, I think people who get stumbling blocks over genealogy questions are sweating waaaaay too much about the small stuff. If you don't want to believe in the general historical accuracy of the Bible, why aren't you worrying about Ajalon? And if you do want to believe, why are you worrying about genealogy tables?
But I think the main problem is that ancient genealogy tables are as much a literary genre as a real source of factual information. Who you-the-writer choose to include, who you choose to leave out, and which generations you elide are pretty much the points of interest here, as well as how the generations are organized. If later readers expect a DNA chart including every Cro-Magnon and Neanderthal involved, they're bound to be sorely disappointed. But that's not the writer's fault.
If you really wanted to know evvvvvery gennnnnneration evvvver, there were probably people in the Jewish community before the destruction of Israel (and hence, the Christian community) in apostolic times who could have told you. Heck, there were still kinfolk of Jesus around. (Well, not the ones who were martyred, and not the ones who were killed by the Romans for being potential foci of rebellion as House of David members.) So why include such easily-obtainable but boring information in a book meant for reading out loud to the congregation?
No, anybody who's in the genealogies in the Gospels is there for a specific reason -- displaying God's plan as carried out down the ages. If we don't get the gist of that, that's our problem.
For example, this site talks about the women in Christ's genealogy, but doesn't explain why these "disreputable women" are there. First off, none of these women are disreputable -- those who sinned repented. Second, all these women represent virtues. Tamar won a son for her dead husband despite his family's unjust opposition and their maltreatment of her. Rahab, a foreigner, was brave and hospitable to strangers and helped Israel win a city, winning her place among them. Ruth, another foreigner, took care of her mother-in-law, brought her dead husband's property back to his clan, and was the classic example of a good woman and wife to Boaz. And Bathsheba, for all her problems, was a fierce and wise queen mother to her son Solomon, helping him rise to kingship and advising him once he got there.
So all these ladies of note, with their checkering of good and evil, convention and innovation, faithfulness and un-, represent Israel itself as well as the spotless Church, Jesus' bride. God helped them bring good out of evil. They also foreshadow the Virgin Mary, because all these women's good deeds and cooperation with God helped the Messiah to come.
That particular site gets pretty weird with its thoughts on Joseph's parentage, btw. Totally glides over the whole Christian tradition that Joseph was the son of a levirate marriage in favor of an explanation from one source, the Jerusalem Talmud. Totally avoids the fact that every other source says Mary is the daughter of Joachim and Anna. Totally avoids the fact that it's as likely that Mary might be the daughter-in-law "daughter of Heli" as that Joseph might be the son-in-law "son of Heli", for that matter.
However, there's some really fun thoughts about Joseph's relationship to Jehoiakim's curse. Worthy of a fantasy novel.
Here's a Greek Orthodox priest who talks about some more of these issues.
The always useful Catholic encyclopedia article has a lot of the sources summarized. This one talks about Biblical genealogy principles. If you're really interested, you can also go diving through Eusebius and learn all about Jesus' kinfolk in the Church.