How can I beat the browser when it comes to reducing image size?

Can't get my head around this. I tried several ways to reduce the pixel size of a logo in Gimp. However, the browser (either safari, firefox or chrome on my iMac) is always amazingly better reducing the logo to the size I specify in the html. Is it really so difficult to beat the browser?

For your information: My base file is an .eps. For Gimp to be able to read the file I converted the format to .tif and .png. I need the intermediate step of Gimp because I need to make the background of the image transparent.