I am trying to decrease bootstrap 3.0 navbar height which is used with fixed top behavior. Here i am using code.
HTML
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: