Decreasing height of bootstrap 3.0 navbar

Working solution:

Bootstrap 3.0 by default has a 15px padding on top and bottom, so we just need to override it!

For example:

.navbar-nav > li > a {padding-top:10px !important; padding-bottom:10px !important;}
.navbar {min-height:40px !important}

Simply override the min-height set in .navbar like so:

.navbar{
  min-height:20px; //* or whatever height you require
}

Altering an elements height to something smaller than the min-height won't make a difference...

After spending few hours, adding the following css class fixed my issue.

Work with Bootstrap 3.0.*

.tnav .navbar .container { height: 28px; }

Work with Bootstrap 3.3.4

.navbar-nav > li > a, .navbar-brand {
    padding-top:4px !important; 
    padding-bottom:0 !important;
    height: 28px;
}
.navbar {min-height:28px !important;}

Update Complete code to customize and decrease height of navbar with screenshot.

CSS:

/* navbar */
.navbar-primary .navbar { background:#9f58b5; border-bottom:none; }
.navbar-primary .navbar .nav > li > a {color: #501762;}
.navbar-primary .navbar .nav > li > a:hover {color: #fff; background-color: #8e49a3;}
.navbar-primary .navbar .nav .active > a,.navbar .nav .active > a:hover {color: #fff; background-color: #501762;}
.navbar-primary .navbar .nav li > a .caret, .tnav .navbar .nav li > a:hover .caret {border-top-color: #fff;border-bottom-color: #fff;}
.navbar-primary .navbar .nav > li.dropdown.open.active > a:hover {}
.navbar-primary .navbar .nav > li.dropdown.open > a {color: #fff;background-color: #9f58b5;border-color: #fff;}
.navbar-primary .navbar .nav > li.dropdown.open.active > a:hover .caret, .tnav .navbar .nav > li.dropdown.open > a .caret {border-top-color: #fff;}
.navbar-primary .navbar .navbar-brand {color:#fff;}
.navbar-primary .navbar .nav.pull-right {margin-left: 10px; margin-right: 0;}
.navbar-xs .navbar-primary .navbar { min-height:28px; height: 28px; }
.navbar-xs .navbar-primary .navbar .navbar-brand{ padding: 0px 12px;font-size: 16px;line-height: 28px; }
.navbar-xs .navbar-primary .navbar .navbar-nav > li > a {  padding-top: 0px; padding-bottom: 0px; line-height: 28px; }
.navbar-sm .navbar-primary .navbar { min-height:40px; height: 40px; }
.navbar-sm .navbar-primary .navbar .navbar-brand{ padding: 0px 12px;font-size: 16px;line-height: 40px; }
.navbar-sm .navbar-primary .navbar .navbar-nav > li > a {  padding-top: 0px; padding-bottom: 0px; line-height: 40px; }

Usage Code:

<div class="navbar-xs">
   <div class="navbar-primary">
       <nav class="navbar navbar-static-top" role="navigation">
          <!-- Brand and toggle get grouped for better mobile display -->
          <div class="navbar-header">
              <button type="button" class="navbar-toggle" data-toggle="collapse" data-target="#bs-example-navbar-collapse-8">
                 <span class="sr-only">Toggle navigation</span>
                 <span class="icon-bar"></span>
                 <span class="icon-bar"></span>
                 <span class="icon-bar"></span>
              </button>
              <a class="navbar-brand" href="#">Brand</a>
          </div>
          <!-- Collect the nav links, forms, and other content for toggling -->
          <div class="collapse navbar-collapse" id="bs-example-navbar-collapse-8">
              <ul class="nav navbar-nav">
                  <li class="active"><a href="#">Home</a></li>
                  <li><a href="#">Link</a></li>
                   <li><a href="#">Link</a></li>
              </ul>
          </div><!-- /.navbar-collapse -->
      </nav>
  </div>
</div>