How can I produce better spacing between header and content when using fancyhdr package?

Question

I am currently using the fancyhdr package with the following setup:

%BOOK FORMATTING
\usepackage{fancyhdr}                       % nice header format
    \fancyhead[RO, LE]{\textbsf{\thepage}}      % page numbers, on both odd and even
    \fancyhead[LO]{\textbsf{\leftmark}}         % chapter headings
    \fancyhead[RE]{\textbsf{\rightmark}}        % section headings

with the \pagestyle{fancy} option. This produces the following output:

However, I require more space between the header and the main content because it looks a little cramped right now. Sometimes, also, Large font sizes trespass through the header, which is unsightly, although I couldn't find an example of this in my current document.

How can I introduce more space between the header and main content?

Desired output: