A further 20% entered through preferences given to other family members.
That left just 14% who were sponsored by companies, about the same share who first entered the country as refugees or asylum-seekers (a further 5% were lottery winners).
Despite this bias towards families, the share of immigrants who arrived with degrees has risen from 27%, for those who arrived between and 1986 and 1990, to almost half now.
America is not the only rich country to have seen such an increase.
According to the OECD (a club of mostly wealthy countries), the number of college-educated migrants heading to member countries grew by 70% between 2001 and 2011.
Recent migrants to America are as likely to be highly educated as those who move to Europe are.
They still lag some way behind Australia and Canada, though.
The result is that America has switched from importing people who are, on average, less educated than the natives to people who are better schooled.
Most states gained in college-educated immigrant populations between 2010 and 2015.
Immigrants were more educated than Americans in 26 states.
“This shift has gone unnoticed by the broader population and policymakers,” says Ms Batalova of the MPI.
Many people have an outdated notion of who immigrants are, conflating them with the undocumented.
The number of undocumented migrants has been falling, but even they are more likely to have a degree these days: the MPI reckons that a fifth of graduate immigrants are undocumented.
Nearly a third of refugees have at least one degree.
One difficulty even educated migrants face on arrival is that employers do not always recognise foreign degrees and experience abroad.
Antiquated licensing requirements and regulations also help.
Upwardly Global, a charity which helps skilled immigrants translate their CVs into American, cites the example of a former Medecins Sans Frontieres doctor from Botswana who worked as a waiter until he got help to navigate the system.
As for Mr Rommel Umano, despite his years as an architect and two degrees, he had a hard time getting work in his profession in America.
Needing money, he took a job loading boxes in a New Jersey warehouse two hours away from his home in the Bronx.
The charity polished his CV and put him through mock interviews and in touch with his current employer, a construction firm.
There, he says the work is pretty similar to what he was doing in Japan.