I've got this

** The quick red fox

   #+BEGIN_QUOTE
   red foxes are great
   #+END_QUOTE

   jumped over the lazy brown dog.

But when I export to HTML I see the

<div id="outline-container-orgheadline5" class="outline-3">
   <h3 id="orgheadline5">
      <span class="section-number-3">1.5</span>
           The quick red fox
    </h3>
    <div id="text-1-5" class="outline-text-3">
       <blockquote>
            <p>Red foxes are great.</p>
       </blockquote>
       <p> jumped over the lazy brown dog.</p>
   </div>
</div>

That is, the export is introducing <p> when the level's text resumes after
the quote, forcing me to pick through my style.css and change everything
individually, e.g., font-size. What I need is for the "jumped over the lazy
dog." to not be in <p></p> under the <div id="text-1-5"
class="outline-text-3"> but outside it, i.e., at the same level as the
first block of text. Basically, I want a way to insert quotes, code blocks,
whatever and not have it twist up the HTML.

LB