(written from a Production point of view)
As it became clear that the Dominion would play an integral part as a continuous threat in the Star Trek: Deep Space Nine series, the role of their foot soldiers, the Jem'Hadar, had to be upgraded to emulate the Star Trek: The Next Generation's uncompromising, implacable and daunting Borg. While the previously introduced Jem'Hadar fighter filled to some extent that role, a larger capital ship was called for, which the Jem'Hadar eventually received in the guise of the Jem'Hadar battle cruiser
For the episodes "In Purgatory's Shadow" and "By Inferno's Light" the script called for a new large Jem'Hadar ship. John Eaves was given the task of designing the ship in 1996. Eaves got his inspiration from the Douglas A-4 Skyhawk aircraft when designing the battle cruiser, "For the Jem Hedar/Dominion battle cruiser, the A-4 played a major role in the overall look of the ship. This was one of the first war ships that I got to work on during the 4 years on at DS9, For DS my primary job was props and work would spill over into some fun vessel projects every once in a while." Eaves produced a 3/4 view that was quickly approved, "(...)usually it's the 3/4 so I can see most of what is going on in one drawing!!! it's the fastest way to get a big overview of what your trying to create.(...)this one image was about it!!! I did a rough blue of what you see here, it made a quick approval and went right to ink(...)."
Physical studio models
A physical model was deemed necessary for close-up shots. Byu this time, Brazil-Fabrication & Design was no longer available to the franchise, and an outside contarctor was approached. The model, measuring 48×48 inches, was eventually built by Don Pennington , or as Visual Effects Supervisor David Stipes for the episode has put it, "John Eaves generated top, bottom, front and side drawings, that VisionArt used to create the CGI ship. Animator Tony Sansalone did the work. Concurrently a model maker named Don Pennington was building a dimensional version. So we wound up building two ships, a physical version and a computer version..." (Cinefantastique, Vol.29, No.6/7, p. 39) Due to budget constraints, the internally lit model was built from traditional material, cast resin with plastic elements, as the newer light weight composites were outside of the budget, resulting in a heavy and cumbersome model. "The model was very large and with traditional materials it became very heavy. It took three to four people to safely lift and turn the model over for various shots. It was affectionately dubbed the "Lead Hadar". (The nick-name was earned; I know first hand as I got to help turn it over once.)", Stipes jokingly remembered. It proved to be the next to last specifically built physical starship studio model for televised Star Trek (the models built later for "A Time to Stand", being "kitbashes") and was used in subsequent episodes of Deep Space Nine, debuting in "Ties of Blood and Water" and for the last time appearing in "Sacrifice of Angels" as stock footage.
The Jem'Hadar battle cruiser model (measuring 48×48 inches) was listed in the 40 Years of Star Trek: The Collection auction as Lot 484, with an estimated sale price of US$2,000-$3,000; it sold on 6 October 2006 for US$6,000 ($7,200 with premium). A foam core camera test model sold as Lot 8459 in August 2008 for US$204.73 in a It's A Wrap! sale and auction.
A reportedly second Jem'Hadar battle cruiser studio model, in a slightly different paint scheme, but not internally lit, showed up as Lot 1487 in the Profiles in History's Hollywood Auction 40 of 12 June 2010, estimated at US$6,000-$8,000.wbm, but was pulled at the last minute from the auction without further clarification, as doubts arose about the claim that the model was actually screen-used and owned by the studio.  The retraction was a result of aficionado's Alec Peters scrutiny, who proved this item to be a display piece for Pennington's own effects shop.  Nevertheless, this model eventually did wind up in the collection of an American collector outside the auction circuit , who discovered upon receival of the model, that some parts of it were were in fact the master templates from which the parts were taken to construct the actual studio model. 
As touched upon by Stipes, he felt that the intricate scene of the Jem'Hadar fleet approaching through, and interacting with, the wormhole could only be executed as a CGI effect, so a CGI model of the battle cruiser was concurrently built at VisionArt Design & Animation by Tony Sansalone. It made the design one of the very few, if not only, that was executed simultaneously as a physical as well as a digital variation. The digital model had a slightly different design as its nacelle struts were attached to the hull at a somewhat steeper angle. Some slight visual differences existed between the CGI model that appeared in "By Inferno's Light", and the CGI cruiser that later appeared in "Sacrifice of Angels". Despite these differences, namely the angle of the nacelles in relation to the hull, the two designs were, in actuality, intended to be the same ship. Confirmation of this was explained by DS9 Visual Effects Supervisor David Stipes at alt.tv.star-trek.ds9. There, Stipes would further clarify that "there are differences that come from changes in the CGI model to make it match the physical model. Remember, the CGI work for these shows were done by different companies at different times."
For the episode "Sacrifice of Angels", in which the physical model was also featured for a last time, VisionArt's CGI model was reprogrammed and remapped in the LightWave 3D software at Foundation Imaging by Michael Stetson under supervision of Ron Thornton. (Sci-Fi & Fantasy Models, issue 32, 1998, p. 53)
The differences between the two designs, in fan circles referred to as the "V-type" and "U-type", may well have stemmed from misinterpretation of Eaves' original design sketches. By this time production of full orthographic blueprints has become uncustomary for the television productions. As Eves explained in regard to an earlier design of his,"Most of the time with models all you need is a three-quarter view, and a couple of three-quarter angles on different parts of the ship." (Star Trek: The Magazine Volume 1, Issue 2, p. 22). While reprogramming VisionArt's CGI model, Stetson, who had the physical studio model at his disposal as reference, made use of the opportunity to correct the the angle of the nacelle struts, to have it correspond with that of the physical model.