diff --git a/test-suite/tests/nw-err-xs0001-002.xml b/test-suite/tests/nw-err-xs0001-002.xml
index 6e81de12..47fa9b2b 100644
--- a/test-suite/tests/nw-err-xs0001-002.xml
+++ b/test-suite/tests/nw-err-xs0001-002.xml
@@ -4,6 +4,15 @@
 <t:info>
   <t:title>Test err:XS0001 002</t:title>
   <t:revision-history>
+    <t:revision>
+      <t:date>2024-11-11</t:date>
+      <t:author>
+        <t:name>Norman Walsh</t:name>
+      </t:author>
+      <t:description xmlns="http://www.w3.org/1999/xhtml">
+        <p>Fixed test. Atomic steps can self-referentially refer to their own output.</p>
+      </t:description>
+    </t:revision>
     <t:revision>
       <t:date>2018-10-16</t:date>
       <t:author>
@@ -22,9 +31,15 @@
 
 <t:pipeline>
   <p:declare-step xmlns:p="http://www.w3.org/ns/xproc" version="3.0">
-    <p:identity name="step">
+    <p:identity name="step-a">
+      <p:with-input port="source">
+        <p:pipe step="step-b" port="result"/>
+      </p:with-input>
+    </p:identity>
+
+    <p:identity name="step-b">
       <p:with-input port="source">
-        <p:pipe step="step" port="result"/>
+        <p:pipe step="step-a" port="result"/>
       </p:with-input>
     </p:identity>
   </p:declare-step>
diff --git a/test-suite/tests/nw-err-xs0001-003.xml b/test-suite/tests/nw-err-xs0001-003.xml
index de953809..ea5f7602 100644
--- a/test-suite/tests/nw-err-xs0001-003.xml
+++ b/test-suite/tests/nw-err-xs0001-003.xml
@@ -4,6 +4,15 @@
 <t:info>
   <t:title>Test err:XS0001 003</t:title>
   <t:revision-history>
+    <t:revision>
+      <t:date>2024-11-11</t:date>
+      <t:author>
+        <t:name>Norman Walsh</t:name>
+      </t:author>
+      <t:description xmlns="http://www.w3.org/1999/xhtml">
+        <p>Fixed test. Atomic steps can self-referentially refer to their own output.</p>
+      </t:description>
+    </t:revision>
     <t:revision>
       <t:date>2018-10-16</t:date>
       <t:author>
@@ -22,11 +31,13 @@
 
 <t:pipeline>
   <p:declare-step xmlns:p="http://www.w3.org/ns/xproc" version="3.0">
-    <p:count name="step">
-      <p:with-option name="limit" select="10">
-        <p:pipe step="step" port="result"/>
+    <p:input port="source"/>
+    <p:count name="step-a">
+      <p:with-option name="limit" select="count(/*)">
+        <p:pipe step="step-b" port="result"/>
       </p:with-option>
     </p:count>
+    <p:identity name="step-b"/>
   </p:declare-step>
 </t:pipeline>
 </t:test>
diff --git a/test-suite/tests/nw-err-xs0001-005.xml b/test-suite/tests/nw-err-xs0001-005.xml
deleted file mode 100644
index d068fe94..00000000
--- a/test-suite/tests/nw-err-xs0001-005.xml
+++ /dev/null
@@ -1,43 +0,0 @@
-<t:test xmlns:t="http://xproc.org/ns/testsuite/3.0"
-        xmlns:err="http://www.w3.org/ns/xproc-error"
-        expected="fail" code="err:XS0001">
-<t:info>
-  <t:title>Test err:XS0001 005</t:title>
-  <t:revision-history>
-    <t:revision>
-      <t:date>2019-07-20</t:date>
-      <t:author>
-        <t:name>Achim Berndzen</t:name>
-      </t:author>
-      <t:description xmlns="http://www.w3.org/1999/xhtml">
-        <p>Fixed test by declaring output port on p:viewport.</p>
-      </t:description>
-    </t:revision>
-    <t:revision>
-      <t:date>2018-10-16</t:date>
-      <t:author>
-        <t:name>Norman Walsh</t:name>
-      </t:author>
-      <t:description xmlns="http://www.w3.org/1999/xhtml">
-        <p>Initial commit</p>
-      </t:description>
-    </t:revision>
-  </t:revision-history>
-</t:info>
-<t:description xmlns="http://www.w3.org/1999/xhtml">
-  <p>Tests that <code>err:XS0001</code> is raised if a pipeline contains
-  a loop.</p>
-</t:description>
-
-<t:pipeline>
-  <p:declare-step xmlns:p="http://www.w3.org/ns/xproc" version="3.0">
-    <p:viewport name="step" match="doc">
-      <p:output port="result" />
-      <p:with-input>
-        <p:pipe step="step" port="result"/>
-      </p:with-input>
-      <p:identity/>
-    </p:viewport>
-  </p:declare-step>
-</t:pipeline>
-</t:test>
diff --git a/test-suite/tests/nw-err-xs0001-007.xml b/test-suite/tests/nw-err-xs0001-007.xml
deleted file mode 100644
index 5205400d..00000000
--- a/test-suite/tests/nw-err-xs0001-007.xml
+++ /dev/null
@@ -1,34 +0,0 @@
-<t:test xmlns:t="http://xproc.org/ns/testsuite/3.0"
-        xmlns:err="http://www.w3.org/ns/xproc-error"
-        expected="fail" code="err:XS0001">
-<t:info>
-  <t:title>Test err:XS0001 007</t:title>
-  <t:revision-history>
-    <t:revision>
-      <t:date>2018-10-16</t:date>
-      <t:author>
-        <t:name>Norman Walsh</t:name>
-      </t:author>
-      <t:description xmlns="http://www.w3.org/1999/xhtml">
-        <p>Initial commit</p>
-      </t:description>
-    </t:revision>
-  </t:revision-history>
-</t:info>
-<t:description xmlns="http://www.w3.org/1999/xhtml">
-  <p>Tests that <code>err:XS0001</code> is raised if a pipeline contains
-  a loop.</p>
-</t:description>
-
-<t:pipeline>
-  <p:declare-step xmlns:p="http://www.w3.org/ns/xproc" version="3.0">
-    <p:for-each name="step">
-      <p:with-input>
-        <p:pipe step="step" port="result"/>
-      </p:with-input>
-      <p:output port="result"/>
-      <p:identity/>
-    </p:for-each>
-  </p:declare-step>
-</t:pipeline>
-</t:test>