More research that my husband and I are learning about are the independent adoptions.
Here is an article from Adoption.com:
Are identified or designated adoptions where prospective adopting and prospective placing parents have located each other themselves (allowed in most States, and some agencies will assist with these placements); using attorneys or other intermediaries defined by State law; using adoption facilitators (allowed in only a few states and some foreign countries); doing the work yourself (permitted for some international adoptions) with the aid of in-country assistance.
Since adoption laws in the state where you live govern your options, it is essential that you know what types of placements are allowed or not allowed by your state’s laws. If you pursue an adoption across state lines, you must comply with the laws in both states before the child can join your family. States have enacted legislation that governs how children can be placed across State lines (Interstate Compacts).
For international adoptions, your state laws, laws and regulations of the U.S. Citizenship and Immigration Service (USCIS, formerly INS), the U.S. State Department, and the laws of the specific country will apply.
In weighing your options, you should evaluate your ability to tolerate risk.
Of the options outlined above:
agency adoptions provide the greatest assurance of monitoring and oversight since agencies are required to adhere to licensing and procedural standards;
independent adoptions by attorneys at least provide assurance that attorneys must adhere to the standards of the Bar Association and some attorneys who specialize in adoption are members of the American Academy of Adoption Attorneys, a professional membership organization with standards of ethical practice;
adoptive placements by facilitators offer the least amount of supervision and oversight. This does not mean that there are not ethical professionals with good standards of practice; it simply means there are few or no oversight mechanisms in place at this time.
In addition to risk factors above, other considerations in selecting the type of adoption you pursue can include:
>>> country restrictions (international adoptions)
>>> open adoptions
>>> child health
>>> your age, marital status, sexual orientation, etc.