diff --git a/src/vimtutor b/src/vimtutor
index 2fbb137..731b1ef 100755
--- a/src/vimtutor
+++ b/src/vimtutor
@@ -39,18 +39,22 @@
 # remove the copy of the tutor on exit
 trap "rm -rf $TODELETE" 0 1 2 3 9 11 13 15
 
-# Vim could be called "vim" or "vi".  Also check for "vim6", for people who
-# have Vim 5.x installed as "vim" and Vim 6.0 as "vim6".
-testvim=`which vim6 2>/dev/null`
-if test -f "$testvim"; then
-	VIM=vim6
-else
-	testvim=`which vim`
+# Vim could be called "vim" or "vi".  Also check for "vimN", for people who
+# have Vim installed with its version number.
+# We anticipate up to a future Vim 8 version :-).
+seq="vim vim8 vim75 vim74 vim73 vim72 vim71 vim70 vim7 vim6 vi"
+for i in $seq; do
+	testvim=`which $i 2>/dev/null`
 	if test -f "$testvim"; then
-		VIM=vim
-	else
-		VIM=vi
+		VIM=$i
+		break
 	fi
+done
+
+# When no Vim version was found fall back to "vim", you'll get an error message
+# below.
+if test -z "$VIM"; then
+	VIM=vim
 fi
 
 # Use Vim to copy the tutor, it knows the value of $VIMRUNTIME