"I deeply appreciate the comprehensive study of this long-standing ethical problem which your paper presented.  It is by far the best analysis and examination I have seen.  I’m grateful to have found it in my preparation to teach 1 Samuel 15 Sunday.

"It seems to me you may have overstated the case for Amalekites being accepted as emigrants into Israel.  I find the young man in 2 Samuel 1 as the only example, and it doesn’t seem clear whether he was a soldier under Saul, a POW set free accidentally in the confusion of battle, or what.  We do have the examples of Rahab and Ruth, but of course they were not Amalekites.  Do you have any further example or clarification at this point?

We don't have many specific examples of non-Israelites mentioned in the bible, but the extensive legal directives about 'one law for the native born and for the foreigner living among you' create the presumption of a large body of 'resident aliens' protected by God's law--without restriction as to nationality.
 
Here's some quick data from 2 resources, and I will comment on these in a minute:

"The Mosaic legislation was quite open to receive outsiders into the covenant community (hence the LXX rendering of ger proselytos). Certain rights were conceded to them, including sabbatical rest (Ex. 20:10; 23:12; Dt. 5:14), a fair trial (1:16), access to the cities of refuge (Nu. 35:15; Josh. 20:9), and participation in the Feasts of Booths and Weeks (Dt. 16:11, 14). Their sustenance was to be guaranteed by provision for gleaning (along with other needy groups, Lev. 19:10; 23:22), by the triennial tithe (Dt. 26:11f) and by the produce of the land during the Sabbatical Year (Lev. 25:6f). Indeed, the juxtaposition of ger with "native of the land" (e.g., Ex. 12:19, 48), "your countrymen" (lit "your brother"), "sons of Israel," and similar expressions clearly indicates that sojourners were to be treated for the most part just like ordinary Israelites. Their privileges and responsibilities thus included observing the Day of Atonement (Lev. 16:29), the Passover (Ex. 12:49; Nu. 9:14), Unleavened Bread (Ex. 12:19); sacrificial procedures (Lev. 17:8; 22:18; Nu. 15:14–16); atonement for unintentional and defiant sin (15:26–31); purification rites after eating unclean meat (Lev. 17:15; Nu. 19:10), sacrifices to Molech (Lev. 20:2); blaspheming the name of the Lord (24:16), sexual and moral purity (18:26), lex talionis (24:20–22). Lev. 19:33f summarized the idealized position of the gerger’s position was so secure that his prosperity could conceivably exceed that of the native Israelites, and the latter could become servants for the former (Lev. 25:47–55). Covenantal infidelity would bring these conditions as a curse upon Israel (Dt. 28:43). ... Such rights and privileges only accrued to the sojourner following complete identification with the covenant community, including circumcision (Ex. 12:43–47). Those who refused were treated as foreigners. Whereas Lev. 17:15 forbids the native and the ger to eat animals that have died a natural death, Dt. 14:21 suggests that such animals could be given to the ger or sold to foreigners for consumption. Rather than treating the former reference as a postexilic development, in which the ger’s status had improved greatly, as is commonly done, the conjoining of ger with norî suggests that the term is not being used technically, the allusion apparently being to an uncircumcised ger. ... At an early period Israel probably adhered to these ideals (Dt. 29:10f [MT 9f]; cf. also 31:12, which included the sojourners in the assembly of those gathered for instruction in the Torah and the fear of the Lord). The gerîm were also present at the covenant renewal ceremony conducted at Mt. Ebal and Mt. Gerizim (Josh. 8:33). ... Second-class treatment of sojourners may, however, be documented from later history. The gêrîm noted separately in David’s census (2 Ch. 2:17 [MT 16]) became the basis of Solomon’s work crews, some of which consisted entirely of sojourners (cf. 1 Ch. 22:2). Nevertheless, in Ezekiel’s vision of the restored community (47:22), the identification of the gêrîm with native Israelites is almost complete, even to receiving an inheritance of land in the midst of the tribe in which they resided. [ISBE]

"Foreigners or sojourners had certain rights but also certain limitations while in Israel. They could offer sacrifices (Lv 17:8; 22:18) but could not enter the sanctuary unless circumcised (Ez 44:9). They were allowed to participate in the three great Jewish festivals (Dt 16:11, 14) but could not eat the Passover meal unless circumcised (Ex 12:43, 48). Foreigners were not obliged to follow the Israelite religion, but shared in some of its benefits (Dt 14:29). They were not to work on the sabbath and the Day of Atonement (Ex 20:10; 23:12; Lv 16:29; Dt 5:14) and could be stoned for reviling or blaspheming God’s name (Lv 24:16; Nm 15:30). Foreigners were forbidden to eat blood (Lv 17:10, 12) but could eat animals that had died a natural death (Dt 14:21). Israel’s code of sexual morality also applied to the foreigner (Lv 18:26). There were prohibitions against Israelite intermarriage with foreigners, but it was nevertheless a common occurrence (Gn 34:14; Ex 34:12, 16; Dt 7:3, 4; Jos 23:12). ...Civil rights were provided for foreigners by the Law of Moses (Ex 12:49; Lv 24:22), and they came under the same legal processes and penalties (Lv 20:2; 24:16, 22; Dt 1:16). They were to be treated politely (Ex 22:21; 23:9), loved as those under the love of God (Lv 19:34; Dt 10:18, 19), and treated generously if poor and receive the fruits of the harvest (Lv 19:10; 23:22; Dt 24:19–22). They could receive asylum in times of trouble (Nm 35:15; Jos 20:9). Foreign servants were to receive treatment equal to Hebrew servants (Dt 24:14). A foreigner could not take part in tribal deliberations or become a king (17:15). The prophet Ezekiel looked forward to the messianic age when the foreigner would share all the blessings of the land with God’s own people (Ez 47:22, 23) in Israel. . [Baker Ency of the Bible, 'alien']

The only stated restrictions, btw, that are ever mentioned are those for which God made exceptions(!): no Moabite (Ruth), no Ammonite (Rehoboam's mother was an Ammonite wife--for good or mostly ill--of Solomon, so Ammonite blood went into the Davidic line at that point--like Moabite blood had earlier), no Canaanite (Rahab), and no Amalekite (the case in 2 Sam, by my reading).
 
[Even the forbidden-from-worship eunuch would have a place in the future kingdom, even though we don't have examples in the OT: see Deut 23.1 followed by Is 56.3-5, which includes the foreigner.]
 
The 'foreign rabble' that came out of Egypt with Israel (that helped get them into trouble!) is also part of the backdrop of God's acceptance of foreigners--of whatever background--into the community (but not the 'communion') of Israel in the land.
 
We also have the case of the runaway slave, who is allowed to dwell anywhere in the land he chooses--without ethnic/national exclusions.
 
In the specific passage I was discussing, let me explain my reading. On the Amalekite's status, btw, I take the first part of his statement ("I am the son of a sojourner...") to identify him as being an immigrant--even though the rest of his testimony is clearly false. He might have been a mercenary in Saul's army [Eglon of Moab used Amalekite mercenaries], but that would not exclude him from being the son of a sojourner, of course. [If he were a solider in the victorious Philistine army--as some commentators take him--he wouldn't have come to court David's favor, IMO.] It was the falsehood part of his statement that he was trying to use to win David's approval--his status as 'son of sojourner' wouldn't necessarily have been to gain favor... and his self-identification as an Amalekite would not have been a ploy to gain David's approval either(!!), of course. So, I don't see any reason for falsehood in the identification part of his statement--only in the latter. (And David's presumption that the Amalekite understood about 'the LORD's anointed' -although it could have been an ironic statement to prove to the Amalekite that he was not a truly-integrated sojourner--still makes me think David accepted his identification as 'the son of a sojourner' as being accurate.). So, it's the 'son of a sojourner' phrase that tips the scales for me, into believing this man was at least the SON of an immigrant Amalekite. Note, though, that he doesn't indicate that he himself was a 'sojourner'--but this might have been just to emphasize the 2nd-generation 'stronger' status of his position.
 

I should also mention that I cannot think of a single other ENEMY of Israel in the OT (of any scale) that we do not have at least one example of a 'favorable' or 'friendly' contact from that group. Uriah the Hittite is a good example. Even though he was a soldier, he was obviously well-integrated into Israel at some level. Bathsheba his wife/widow was probably the granddaughter of David/Absalom's famous counselor Ahithophel. Nahash the Ammonite king took care of David's family during his persecution by Saul. Araunah the Jebusite, Ittai the loyal Philistine friend/supporter of David from Gath (2 Sam 15), etc. Even the hated Edomites are mentioned as a covenant partner of the Lord (e.g. Deut 2.1-8), and participated in military alliances WITH--not always against!--Israel (2 kings 3).
 
It is not that these people are 'sojourners' but rather that the 'ethnic boundaries' of Israel and the community, or the relationship-area 'around' her were perhaps a bit more porous than we might otherwise suspect. And that the lack of a specific people's mention (e.g. another mention of Amalek) would NOT be an indication of their exclusion from this general 'openness' of biblical Israel to sincere immigration desires. just FWIW.