diff --git a/libexec/rtld-elf/libmap.c b/libexec/rtld-elf/libmap.c
index e710fd586b29..4705bc69d125 100644
--- a/libexec/rtld-elf/libmap.c
+++ b/libexec/rtld-elf/libmap.c
@@ -33,6 +33,7 @@ struct lm {
 TAILQ_HEAD(lmp_list, lmp) lmp_head = TAILQ_HEAD_INITIALIZER(lmp_head);
 struct lmp {
 	char *p;
+	enum { T_EXACT=0, T_BASENAME, T_DIRECTORY } type;
 	struct lm_list lml;
 	TAILQ_ENTRY(lmp) lmp_link;
 };
@@ -42,6 +43,7 @@ static void		lm_free		(struct lm_list *);
 static char *		lml_find	(struct lm_list *, const char *);
 static struct lm_list *	lmp_find	(const char *);
 static struct lm_list *	lmp_init	(char *);
+static const char * quickbasename	(const char *);
 
 #define	iseol(c)	(((c) == '#') || ((c) == '\0') || \
 			 ((c) == '\n') || ((c) == '\r'))
@@ -216,6 +218,8 @@ lm_find (const char *p, const char *f)
 		return (NULL);
 }
 
+/* Given a libmap translation list and a library name, return the
+   replacement library, or NULL */
 #ifdef COMPAT_32BIT
 char *
 lm_findn (const char *p, const char *f, const int n)
@@ -250,6 +254,8 @@ lml_find (struct lm_list *lmh, const char *f)
 	return NULL;
 }
 
+/* Given an executable name, return a pointer to the translation list or
+   NULL if no matches */
 static struct lm_list *
 lmp_find (const char *n)
 {
@@ -258,7 +264,9 @@ lmp_find (const char *n)
 	dbg("%s(\"%s\")", __func__, n);
 
 	TAILQ_FOREACH(lmp, &lmp_head, lmp_link)
-		if (strcmp(n, lmp->p) == 0)
+		if ((lmp->type == T_EXACT && strcmp(n, lmp->p) == 0) ||
+		    (lmp->type == T_DIRECTORY && strncmp(n, lmp->p, strlen(lmp->p)) == 0) ||
+		    (lmp->type == T_BASENAME && strcmp(quickbasename(n), lmp->p) == 0))
 			return (&lmp->lml);
 	return (NULL);
 }
@@ -272,8 +280,28 @@ lmp_init (char *n)
 
 	lmp = xmalloc(sizeof(struct lmp));
 	lmp->p = n;
+	if (n[strlen(n)-1] == '/')
+		lmp->type = T_DIRECTORY;
+	else if (strchr(n,'/') == NULL)
+		lmp->type = T_BASENAME;
+	else
+		lmp->type = T_EXACT;
 	TAILQ_INIT(&lmp->lml);
 	TAILQ_INSERT_HEAD(&lmp_head, lmp, lmp_link);
 
 	return (&lmp->lml);
 }
+
+/* libc basename is overkill.  Return a pointer to the character after the
+   last /, or the original string if there are no slashes. */
+static const char *
+quickbasename (const char *path)
+{
+	const char *p = path;
+	for (; *path; path++)
+	{
+		if (*path == '/')
+			p = path+1;
+	}
+	return p;
+}
diff --git a/share/man/man5/libmap.conf.5 b/share/man/man5/libmap.conf.5
index b89d2e449a31..eb2987e427c7 100644
--- a/share/man/man5/libmap.conf.5
+++ b/share/man/man5/libmap.conf.5
@@ -46,14 +46,44 @@ Dependencies are matched against candidates and replaced with the mappings.
 Constrained mappings may be specified by enclosing the name of the
 executable or library in brackets.
 All mappings following a constraint will only be evaluated for that constraint.
-Currently, constraints
-are matched literally so that an executable with a fully qualified pathname
-will only match the same constraint.
-This means that
+Constraints can be one of three types:
+.Bl -tag -width indent
+.It Exact 
+The constraint is matched literally so that only an executable with an
+identical fully qualified pathname will match the constraint.
+This means that the executable
 .Pa /usr/bin/foo
 will not match a constraint for
-.Pa foo
+.Pa /usr/bin/./foo
 and vise-versa.
+This is the default constraint type.
+.It Basename
+A constraint with no path is matched against the basename of the
+executable.
+.Pa foo
+will match 
+.Pa /bin/foo ,
+.Pa /usr/local/sbin/foo ,
+or any other executable named 
+.Pa foo ,
+no matter what its path is.
+.It Directory
+A constraint with a trailing slash is prefix-matched against the full
+pathname of the executable.
+.Pa /usr/bin/
+will match any executable with a path starting with /usr/bin.
+.El
+.Pp
+Note that the executable path matched against is the 
+.Pa path
+parameter in an 
+.Fn exec*
+function call. 
+The Directory or Exact constraints can only match when the executable
+is called with a full pathname.
+Most programs executed from a shell are run without a full path, via
+.Fn exec*p ,
+so the Basename constraint type is the most useful.  
 .Pp
 WARNING!
 Constrained mappings must never appear first in the configuration file.
@@ -77,19 +107,17 @@ libpthread.so		libpthread.so
 libc_r.so.5		libpthread.so.1	# Everything that uses 'libc_r'
 libc_r.so		libpthread.so	# now uses 'libpthread'
 
-[/usr/local/bin/mplayer]		# 'mplayer' uses libc_r.
+[/tmp/mplayer]		# Test version of mplayer uses libc_r
 libpthread.so.1		libc_r.so.5
 libpthread.so		libc_r.so
 
-[mplayer]
-libpthread.so.1		libc_r.so.5
-libpthread.so		libc_r.so
+[mplayer]		# All other mplayers use libpthread
+libpthread.so.1		libpthread.so.1
+libpthread.so		libpthread.so
 
-[/usr/local/sbin/httpd]			# Apache uses libthr
-libpthread.so.1		libthr.so.1
-libpthread.so		libthr.so
-
-[httpd]
+[/usr/local/jdk1.4.1/]	# All Java 1.4.1 programs use libthr
+			# This works because "javavms" executes
+			# programs with the full pathname
 libpthread.so.1		libthr.so.1
 libpthread.so		libthr.so
 .Ed