Avoid empty elements in XSLT output

I want to map an input XML to another XML, simply writing values from the input to different tags in the output.

As a simple example, the following:

<root1>
  <a1>valA<a1>
  <b1>valB<b2>
</root1>

Needs to become:

<root2>
  <a2>valA</a2>
  <b2>valB</b2>
</root2>

Currently I have the following in my XSLT:

<xsl:apply-templates match="root1" />

<xsl:template match="root1">
  <a2>
    <xsl:value-of select="a1" />
  </a2>
  <b2>
    <xsl:value-of select="b2" />
  </b2>
</xsl:template>

The problem is that I don't want empty tags in my output. If valA and valB are empty, I would get:

<root2>
  <a2></a2>
  <b2></b2>
<root2>

But I want to omit the empty tags. I would have thought that there could be an attribute to xsl:output for this, but there isn't... I came across this question on SO: XSLT: How to exclude empty elements from my result? - but the answer is indirect, it specifies a second stylesheet to strip empty output elements after the first transformation.

I need this to be done with one stylesheet. Surely there must be something more concise then doing:

<xsl:if test="string-length(a1) != 0">
  <a2>
    <xsl:value-of select="a1" />
  </a2>
</xsl:if>

or even:

<xsl:template match="a1[string-length(.) != 0]">
  <a2>
    <xsl:value-of select="." />
  </a2>
</xsl:template>

repeated for each element??