Okay, here is how it's supposed to work (as I understand it):
Let's say on April 1 you go to Able Bank to get pre-approved for a mortgage. An inquiry into your credit is made. The credit score pulled is 750.
On April 3 you go to Baker Bank to see if you can get a better rate. Another inquiry is made. The inquiry from Able Bank is visible, but it's not factored into your score (it's suppressed from scoring). Nothing else has changed on your credit report. The credit score pulled by Baker Bank is 750.
On May 20 you go to Charlie Bank to check rates. Another inquiry is made. Both inquiries from Able and Baker are on your credit report. Since these occurred over 30 days ago, they are factored into scoring. But because they were made within the 45 day window, they are treated as a single inquiry. Nothing else has changed on your credit report. The credit score pulled by Charlie Bank is 745.
On June 30 you go to Delta Bank for one last try at snagging getting a better rate. All three previous inquiries are factored into scoring. The inquiries from April 1 and 3 are scored as single inquiry, because they occurred within a single 45 day window. The May 20 inquiry, however, is factored separately. The net effect is that there are two inquiries affecting your score. Nothing else has changed on your credit report. The score pulled by Delta Bank is 740.
Still need to clarify something that you wrote - you said that you did a pre-approval and then two days later your score from this site was 16 points lower. Are you comparing the score that the lender pulled with the score from here? This is important to understand your situation.
Another thing to point out is the recurring sentence in what I've written above: "Nothing else has changed on your credit report." It is important not just to compare scores, but to compare the credit reports that generate the scores. If something else has changed on your report, even if seemingly subtle, it can have an effect on your score. It's sometimes hard to determine the precise effect of a specific change on your credit report, because changes don't always occur in isolation. Even the scenarios above can't really happen, since as time passes your accounts are going to age, and that alone can affect your score.
The last thing I'll add is that in order for the mortgage inquiries to be treated as above (allowing for the 45 day rate-shopping window and suppression from scoring for 30 days), it's important that the inquiries are properly coded as mortgage inquiries. If not, then they may have an immediate effect on your score.
I hope I got that all correct. If not, someone will step in to fix anything that I've gotten wrong.
