diff --git a/tests/Makefile.am b/tests/Makefile.am
index b372a70..ceb503b 100644
--- a/tests/Makefile.am
+++ b/tests/Makefile.am
@@ -158,7 +158,7 @@ comment8.test \
 comment9.test \
 commen10.test \
 commen11.test \
-comments-in-var-definition.test \
+comments-in-var-defn.test \
 compile.test \
 compile2.test \
 compile_f90_c_cxx.test \
diff --git a/tests/Makefile.in b/tests/Makefile.in
index 5a815c9..7ecfcaa 100644
--- a/tests/Makefile.in
+++ b/tests/Makefile.in
@@ -425,7 +425,7 @@ comment8.test \
 comment9.test \
 commen10.test \
 commen11.test \
-comments-in-var-definition.test \
+comments-in-var-defn.test \
 compile.test \
 compile2.test \
 compile_f90_c_cxx.test \
diff --git a/tests/comments-in-var-definition.test b/tests/comments-in-var-defn.test
similarity index 84%
rename from tests/comments-in-var-definition.test
rename to tests/comments-in-var-defn.test
index 6d6a3e3..b00ee6b 100755
--- a/tests/comments-in-var-definition.test
+++ b/tests/comments-in-var-defn.test
@@ -21,11 +21,20 @@
 
 set -e
 
+cat >> configure.in <<'END'
+AC_OUTPUT
+END
+
 # Use a slash in the comment, because automake takes the dirname
 # of TEXINFO_TEX to compute $(am__TEXINFO_TEX_DIR).
 cat > Makefile.am << 'END'
 TEXINFO_TEX = tex/texinfo.tex    # some comment w/ a slash
 info_TEXINFOS = main.texi
+.PHONY: test
+test:
+	test tex/texinfo.tex = $(TEXINFO_TEX)
+	test -d '$(am__TEXINFO_TEX_DIR)'
+	case '$(am__TEXINFO_TEX_DIR)' in tex|./tex) :;; *) exit 1;; esac
 END
 
 cat > main.texi << 'END'
@@ -41,7 +50,9 @@ $AUTOMAKE
 
 grep TEX Makefile.in # for debugging
 grep '^TEXINFO_TEX *= *tex/texinfo\.tex  *# some comment w/ a slash *$' Makefile.in
-grep '^am__TEXINFO_TEX_DIR *=.*[/ ]tex *$' Makefile.in
-$EGREP 'am__TEXINFO_TEX_DIR.*=.*(comment|#)' Makefile.in && Exit 1
+
+$AUTOCONF
+./configure
+$MAKE test
 
 :
diff --git a/tests/vtexi3.test b/tests/vtexi3.test
index 7f5b92f..34f46c5 100755
--- a/tests/vtexi3.test
+++ b/tests/vtexi3.test
@@ -73,29 +73,29 @@ $AUTOMAKE
 
 day='([1-9]|1[0-9]|2[0-9]|3[01])'
 month='(January|February|March|April|May|June|July|August|September|October|November|December)'
-year='20[0-9][0-9]' # hopefully automake will be obsolete in 80 years ;-)
+year='20[0-9][0-9]' # Hopefully automake will be obsolete in 80 years ;-)
 date="$day $month $year"
 
 do_check ()
 {
-  # basename of the vers*.texi file
+  # Basename of the vers*.texi file.
   vfile=$1
-  # $(srcdir) of the current build
+  # The $(srcdir) of the current build.
   srcdir=$2
-  # vers*.texi must be created in $(srcdir)
+  # The vers*.texi file must be created in $(srcdir).
   $MAKE $srcdir/$vfile.texi
   cat $srcdir/$vfile.texi
-  # EDITION and VERSION are synonyms, as per documentation
+  # EDITION and VERSION are synonyms, as per documentation.
   grep "address@hidden EDITION 7\\.45\\.3a$" $srcdir/$vfile.texi
   grep "address@hidden VERSION 7\\.45\\.3a$" $srcdir/$vfile.texi
-  # check that UPDATED seems right, and that UPDATED and UPDATED-MONTH
-  # are consistent
+  # Check that UPDATED seems right, and that UPDATED and UPDATED-MONTH
+  # are consistent.
   $EGREP "address@hidden UPDATED $date$" $srcdir/$vfile.texi
   vmonth=`grep 'address@hidden UPDATED ' $srcdir/$vfile.texi | awk '{print $4, $5}'`
   grep "address@hidden UPDATED-MONTH $vmonth$" $srcdir/$vfile.texi
-  # check that the vers*.texi file is distributed according
-  # to $(DISTFILES)
-  $MAKE echo-distfiles # for debugging
+  # Check that the vers*.texi file is distributed according
+  # to $(DISTFILES).
+  $MAKE echo-distfiles # For debugging.
   $MAKE -s echo-distfiles | grep "[ /]$vfile\\.texi"
 }
 
@@ -111,10 +111,10 @@ do_check vers1a_2b ..
 # and they must be newer than version.texi, so that make won't try
 # to rebuild them.
 $sleep
-: > ../foobar.info
-: > ../quux.info
-: > ../zardoz.info
-# check that the vers*.texi files are really distributed.
+touch ../foobar.info
+touch ../quux.info
+touch ../zardoz.info
+# Check that the vers*.texi files are really distributed.
 $MAKE distdir
 ls -l $distdir
 diff ../version.texi $distdir/version.texi
diff --git a/tests/vtexi4.test b/tests/vtexi4.test
index 1e5e3b0..69dffb5 100755
--- a/tests/vtexi4.test
+++ b/tests/vtexi4.test
@@ -26,20 +26,22 @@ required='makeinfo tex texi2dvi-o'
 
 set -e
 
-day=`LC_ALL=C date '+%d'`   || Exit 77
-month=`LC_ALL=C date '+%B'` || Exit 77
-year=`LC_ALL=C date '+%Y'`  || Exit 77
-
+case `LC_ALL=C date '+%u'` in
+  [1-7]) date_is_posix=:;;
+      *) date_is_posx=false;;
+esac
+$date_is_posix \
+  && day=`LC_ALL=C date '+%d'` && test -n "$day" \
+  && month=`LC_ALL=C date '+%B'` && test -n "$month" \
+  && year=`LC_ALL=C date '+%Y'`&& test -n "$year" \
+  || { echo "$me: 'date' is not POSIX-complaint enough"; Exit 77; }
 day=`echo "$day" | sed 's/^0//'`
 
-# This test requires a grep the can parse nonprinting characters.
-# BSD 'grep' works from a pipe, but not a seekable file.
-# GNU or BSD 'grep -a' works on files, but is not portable.
-tst=''
-case `echo "$tst" | grep .` in
-  "$tst") ;;
-  *) echo "$me: grep can't parse nonprinting characters" >&2; Exit 77;;
-esac
+# This test requires a grep program that can work on non-text input.
+(echo 'x' | grep x) || {
+  echo "$me: grep doesn't work on input that is not pure text" >&2
+  Exit 77
+}
 
 cat > configure.in << END
 AC_INIT([$me], [123.456])
@@ -58,7 +60,8 @@ cat > Makefile.am << 'END'
 include defs.am
 info_TEXINFOS = foo.texi
 test-grepinfo:
-## Not useless uses of cat; see above comments about grep.
+## Not useless uses of cat: we only tested that grep worked on
+## non-text input when that's given from a pipe.
 	cat $(srcdir)/foo.info | grep 'GREPVERSION=$(my_version_rx)='
 	cat $(srcdir)/foo.info | grep 'GREPEDITION=$(my_version_rx)='
 	cat $(srcdir)/foo.info | grep 'GREPDATE=$(my_date_rx)='