This is a REALLY helpful post dzyg. I thank you for posting it and hope that many people view it. This is a perplexing ID issue which many of us have endured. I just did some research on this very issue, and I came across a cool webpage which helped me a lot with this. It mentions the brown cheek patch of the male House Finch as an ID clue. This was helpful to me. http://www.birdzilla.com/bird-identification/id-skill-development/id-challenges/red-finches.html

Yes, Purple Finches also don't have those brown streaked flanks that are present on House Finches. BN

i had one pair of house finches bring their babys 4 of them last week but they have went somewhere. Had one downey yesterday and a Lewis's woodpecker the day before. only kinds in big numbers are the bullocks orioles and the western tanagers and lots of red wing blackbirds and some grosbeaks. one lone juniper titmouse comes occasionally. and the hummingbirds are rare this year. should have lots of little orioles and tanagers soon as they are nesting now

Do not be too quick to dismiss the lowly sparrow. I grew up on a dairy farm in N.E.Ohio and I have always had a passing interest in bird watching, however like most people I erroneously thought a sparrow is a sparrow, is a sparrow and lumped them into one of two broad categories, song sparrows and house sparrows, all of which were often considered at best a minor nuisance. Last June I officially retired and took up nature photography as a retirement hobby. Over the summer I spent most of my time hiking the woods, meadows and swampy areas, but when the summer birds migrated last fall I then set up feeders and turned my attention to the birds that i could attract. I typically set my camera on a tripod zeroed in on a feeder or a ground feeding location, then I sit motionless with a remote shutter release in my pocket and snap pictures of the birds as they come in. In the course of taking 2 or 300 pictures a day, it goes without saying that I get a lot of shots that contain sparrows as well as the more desirable birds. Later while editing the photos I began to notice that many of the sparrows had what i thought were strange or unusual markings. In early October my Mother presented me with a book called "Birds of Ohio" by McCormac & Kennedy, published by the Lone Pine Press (ISBN 13:978-1-55105-392-9)). From this book I discovered that their are over twenty different species of Sparrows common to Ohio, two of which have red heads such as you describe. I then got another book called "The Sparrows of the united States and Canada published by Princeton University Press (ISBN 13:978-0-125-9897-1) in which they list over 62 species of Sparrows native to the U.S. & Canada. In addition, i learned that the House Sparrow is not native to North America and is officially not listed as a Sparrow, but rather they are listed as "Old World Sparrows" which includes another 37 species that have been introduced to North America, primarily from Europe. From my personal experience I would challenge everyone, rather than seek ways to discourage the lowly Sparrow, take a closer look and you might be amazed at what you see, and if the Sparrows are consuming all the seed in your feeders, do as I have done, put up more feeders because all of God's creatures gotta eat. Currently I am going through 5 30lb bags of wild bird seed a month, not to mention another two bushels of corn that i put in chicken feeders out in the meadow for the wild turkeys but then when i consider how many hours I spend watching those birds, it is really rather cheap entertainment.