Dave was my grandmother Tillie Liebross Wilson's first cousin. He was the only son of Hersch Leib Ett and Perl Wenkert Ett and was born in 1891 in Zaleszczyki, at that time within the Austro-Hungarian Empire (now in Ukraine).
David sailed from Hamburg on the Amerika and arrived in New York Harbor on 10 November 1907.  He first declared his intention to become citizen on 17 September 1912.  He, apparently, never finished that process (I have not found a petition).
On 16 December 1927, Dave completed a Petition for Naturalization based upon his military service during World War I.  The Act of 26 May 1926 (44 Stat. 654. 655) granted that alien veterans of World War I, who has served honorably between 6 April 1917 and 11 November 1918 were to be granted naturalization without having to submit a Declaration of Intent any time within two years after enactment of the Act.  But on 19 December 1927, David Ett's petition for citizenship was turned down. He was deemed ineligible under the Act.
The question for me, has been, "Why did he initially think he was eligible for naturalization and why was he deemed ineligible?"
The answer came from Ancestry's new record set.
Dave was inducted into the army on 8 December 1917. He began his service in Battery C, 306th Field Artillery stationed at Camp Upton, Yaphank, Suffolk County, Long Island, New York. Camp Yaphank was built in 1917 and was officially opened just a days after Dave's induction.  
On 3 January 1918 Dave was assigned to the 4th Infantry, Company M (I'm still looking into this, but I believe they were stationed in Greenville, North Carolina.) It was shortly after this that the military's intentions for Dave started to change.
The President of the United States, since before war was declared, had the authority to control the actions and movements of those deemed "enemy aliens" (defined as those born in countries with which we were at war and who had not naturalized in the United States). At first, only Germans were enemy aliens. Later anyone from the Austria-Hungary was included, as well. So, Dave Ett did not ship out overseas with his Company. By 28 June 1918 he was discharged - an enemy alien.
A newspaper article from the era explained that the military was "weeding out" enemy aliens and would require them to register where they expected to reside within ten days of their discharge.  
Dave's discharge from the military was not considered honorable. So, when he applied for citizenship under the Act of May 26, 1926, he was deemed ineligible for the privilege of expedited naturalization.
Years later he tried again. He was granted citizenship on 18 July 1939. 
It is important to note that this newly available online record set is made of information abstracted from several, now likely missing, sources. Ancestry correctly notes in its background information that the process of abstraction is likely to introduce errors. One such error could be Dave Ett's assignment to the 4th Infantry. This information conflicts with information on his 1927 Petition for Naturalization [see note 3] which indicates he served in "Pt. Co. 5, Inf." Of course this latter document also said he was honorably discharged which, we find, was probably inaccurate.
1. "New York Passenger Lists, 1820-1957," digital images, Ancestry.com (http://www.ancestry.com: accessed 5 September 2009), manifest, Amerika, Hamburg to New York, arriving 10 November 1907, list 37, line 8, Duvid Ett, citing National Archives Microfilm Serial T715.
2. Kings County, New York, Kings County Supreme Court, digital images, FamilySearch.org (https://www.familysearch.org : accessed 19 August 2013), Declaration of Intent, number 27049, vol. 55, page 49, David Ett, 17 September 1912.
3. "New York, Naturalization Records, 1882-1944," database, Ancestry.com (http://www.ancestry.com : accessed 5 July 1009), Petition for Naturalization for David Ett, 16 December 1927, New York, citing United States District Court for the Southern District of New York, National Archives and records Administration Series M1972, Roll 551.
4. U.S. Department of Labor, Fourteenth Annual Report of the Secretary of Labor for the Fiscal Year Ending June 30, 1926 (Washington, D.C.: Government Printing Office) 1926, page 127. Digital image, GoogleBooks.com (http://www.books.google.com : accessed 20 August 2013).
5. 'C' Battery Book, 306th F.A., 77th Div., 1917-1919. Digital image, Internet Archives, OpenLibrary.org (http://www.archive.org/stream/cbatterybook306t00broo#page/8/mode/2up : accessed 20 August 2013), page 9ff.
6. By the way, Camp Upton was also where Irving Berlin served and was the source material for his musical revue Yip Yip Yaphank and its memorable song, "Oh, How I Hate to Get Up in the Morning."
7. "Keep Tab Discharged Soldiers: Enemy Aliens Leaving Army Will Be Registered," Seattle Spokesman-Review, 12 March 1918, digital image, Washington State University Library Digital Collections (http://content.wsulibs.wsu.edu : accessed 20 August 2013).
8. Unfortunately, New York State is, apparently, one of the many states that did not retain these records.
9. U. S. District Court of the Eastern District of New York, Petition for Naturalization number 259528, David Ett, 18 July 1939.