Actually, it's nicer with no text above the logo

sass/_theme_layout.sass

@@ -129,7 +129,7 @@
       background: rgba(255,255,255,.1)
     img.logo
       display: block  // display on its own line all the time
-      margin: 0.85em auto 0
+      margin: 0 auto
       height: auto  // undo badge styling above
       width: auto
       border-radius: 0

sphinx_rtd_theme/layout.html

@@ -96,12 +96,12 @@
     {# SIDE NAV, TOGGLES ON MOBILE #}
     <nav data-toggle="wy-nav-shift" class="wy-nav-side">
       <div class="wy-side-nav-search">
-        <a href="{{ pathto(master_doc) }}" class="icon icon-home"> {{ project }}
         {% if logo %}
           {# Not strictly valid HTML, but it's the only way to display/scale it properly, without weird scripting or heaps of work #}
-          <img src="{{ pathto('_static/' + logo, 1) }}" class="logo" />
+          <a href="{{ pathto(master_doc) }}"><img src="{{ pathto('_static/' + logo, 1) }}" class="logo" /></a>
+        {% else %}
+          <a href="{{ pathto(master_doc) }}" class="icon icon-home"> {{ project }} </a>
         {% endif %}
-        </a>
         {% include "searchbox.html" %}
       </div>