Everest Pro – add text place of search/social icons

When I try to add text or little logos/images via either header top sidebar or header right sidebar, it always makes the header deeper and pushes the main header logo down, which spoils the site. So, how can add text/small image to in the big blank area in right of header and leave the header the same depth? I would be quite happy to not have the search/social icons in the header. http://simonkingconstruction.co.uk/wp/