Then there are the super-savers, those who manage to put away more than 15 percent of their incomes. Only 14 percent — or one out of seven — is able to say that. 

Westerners are doing better at it than fellow Americans elsewhere in the country, especially Southerners. While 31 percent of those in the West are among the more-than-10-percent savers, just 20 percent of Southerners can say the same thing. But Westerners are also doing worse at it than the rest of the country, because that region has the highest percentage of those who don't save at all — 19 percent — than any other region. 

Bankrate.com's Financial Security Index fell a bit from 104.8 in February to 103.7. February was the highest the index has been since it began in late 2010, but March is still its second-highest level. An index above 100 indicates improved financial security compared to the previous year. 

Savings is one of the five factors included in the index, and while it is improving, it's still the weakest link. Still, 24 percent of respondents are more comfortable now with their savings than they were a year ago, compared with 27 percent who are less comfortable. That's the lowest margin so far in the index's history. 

That's a vast improvement compared with the index's early days between 2010 and 2012 – when those who were less comfortable with their savings than they were the previous year outnumbered those who were more comfortable by a margin of three to one.