Getting trained in Structural Integration is not like getting trained in Hot Stones - it can't be accomplished in a single weekend workshop.  It's more like graduate school for bodyworkers.  When you consider that a typical weekend workshop represents 16 CEUs, it would take 18.75 weekends (or 7.5 40 hour weeks) to acquire basic training in structural integration.  Many go on to get advanced training, as well.

The IASI (discussed in the previous article) created a set of minimum standards that a school had to meet for its graduates to be able to join the organization as Professional Structural Integrators.  Those standards were also adopted for determining which schools graduates would be eligible to sit for the Certification Exam for Structural Integrators.

The list of approved schools is found here: http://www.theiasi.org/about.php  

• School Training Requirements
• School Faculty Requirements
• The Schools, In Order by Date of Founding 

School Training Requirements 

Total schooling (basic bodywork and structural integration) must total 650 in-class hours (note the SI Exam prerequisites say 750 hours)

300 hours in the theory, methods and application of Structural Integration including:

• a series process
• the concept of the body as integral with gravity
• the fascial system as the structural organizer
• in-class supervised work on at least 2 models
• students giving and receiving the complete series with classmates under instructor supervision 

The school may require graduation from a structured bodywork program (e.g. massage school) as an entrance requirement, or it may include the following in its own program (continuing education workshops are not acceptable as a substitute):

• 100 hours of anatomy/physiology/kinesiology
• 350 hours total hours including general bodywork, ethics and business practices, and the A&P above. 

School Faculty Requirements

The school's primary faculty (not teaching assistants) need to have both practical and teaching experience:

• 5 years experience sometime in their career as a full time SI practitioner
• Previous teaching experience in any type of school, including as assistant faculty or in a teacher training track program

The Schools, In Order by Date of Founding

• The Rolf Institute®
  Boulder, CO, founded 1971 by Dr. Rolf; current faculty were either trained directly by Dr. Rolf or by her first generation of teachers
  only graduates of the Rolf Institute’s program are legally allowed to call their work Rolfing Structural Integration and themselves Rolfers 
  program length 600 instructional hours (18 months) for graduates of a massage therapy program: 731 instructional hours (24 months) for entry level
• SOMA Institute of Neuromuscular Integration®
  Buckley, WA, founded 1977
• International Professional School of Bodywork (IPSB) SI training
  San Diego, CA, founded 1977
• Hellerwork®, International
  office in Anaheim CA, classes taught in various locations, founded 1978
• The Guild for Structural Integration
  Boulder, CO, founded 1989
• CORE Institute
  Tallahassee, FL, founded 1990
• Institute for Structural Integration
  Miami, FL, founded 1992
• Guild for Therapeutic Bodywork, Inc. (Texas School For Structural Integration?)
  Austin, TX, founded 2000
• Mana Integrative Therapies
  Europe and New Zealand, founded 2000

The following schools I couldn't find the date of founding, so I sorted by the program founder's graduation date, as found in the IASI Practioner Directory

• Kinesis Myofascial Integration
  taught in various locations, office in Walpole (Portland) Maine, founded possibly 1998
  Tom Myers - Rolf Institute graduate on 11/01/1976
• Northwest Center for Structural Integration
  Portland, OR & San Juan Islands in WA
  Larry Kaufman - Rolf Institute graduate on 6/08/1979
• Institute of Structural Medicine
  Twisp, WA (east of the North Cascades), founded possibly 2004
  Donna Bajelis - Hellerwork graduate on 12/20/1987
• The School of Integrative Therapies, SI program
  Holmdel, NJ
  Chuck Carpenter - Rolf Institute graduate on 11/17/1989
• Institut fur Strukturelle Korpertherapie translated as Structural Core Therapy Institute
  Nürnberg, Germany
  Dr. Herbert Grassman - The Guild graduate on 5/26/1994

The school Ida Rolf founded, the Rolf Institute of Structural Integration had some of its teachers leave and form new schools even before Ida Rolf's death in 1979.  In some cases, the parting of the ways was friendly, but in others factionalization and schism among those Rolf had certified to teach led to the new schools.  As a result, today there are a number of schools where Structural Integration can be learned, although only graduates of the Rolf Institute’s program are legally allowed to call their work Rolfing Structural Integration and themselves Rolfers. 

When Darren Buford interviewed Tom Myers, Tom gave a great synopsis of how various people split off and formed their own schools:

"When Ida Rolf formed the Rolf Institute, Boulder became the training center for Rolfers. Over the years, various people split off: Joseph Heller broke off and formed Hellerwork; Bill Williams splintered off and formed a similar school called SOMA; CORE; and there was postural integration; rebalancing. You name it, there were several of these Rolf spinoff schools turning out graduates."
...
"In the early '90s, the Rolf Institute itself fractionated with some of Ida Rolf's original teachers going off and forming the Guild for Structural Integration. And others of Ida Rolf's teachers stayed with the Rolf Institute. There's kind of the feeling that the Guild is the Ivory Tower keeping the flame alive, keeping things how it was when Ida Rolf died, or what Ida Rolf intended, and the Rolf Institute saying, "Well that's all very good, but we have to keep developing. Ida was developing all her life and she wouldn't want to keep it frozen." So we have these ideas coming in from osteopathy, from visceral manipulation, from these other places, so it was kind of the purists versus the developers which is a common kind of split among organizations."