diff --git a/src/util.c b/src/util.c
index fada69c..76c4de3 100644
--- a/src/util.c
+++ b/src/util.c
@@ -1960,13 +1960,11 @@ char *format_timespan(char *buf, size_t l, usec_t t) {
                 { "d", USEC_PER_DAY },
                 { "h", USEC_PER_HOUR },
                 { "min", USEC_PER_MINUTE },
-                { "s", USEC_PER_SEC },
-                { "ms", USEC_PER_MSEC },
-                { "us", 1 },
         };
 
         unsigned i;
         char *p = buf;
+        int k;
 
         assert(buf);
         assert(l > 0);
@@ -1983,7 +1981,6 @@ char *format_timespan(char *buf, size_t l, usec_t t) {
         /* The result of this function can be parsed with parse_usec */
 
         for (i = 0; i < ELEMENTSOF(table); i++) {
-                int k;
                 size_t n;
 
                 if (t < table[i].usec)
@@ -2001,6 +1998,10 @@ char *format_timespan(char *buf, size_t l, usec_t t) {
                 t %= table[i].usec;
         }
 
+        /* We have left a value between 0 and 59,999,999 (that is, 0s and 59.999999s) */
+        k = snprintf(p, l, "%s%llu.%06llus", p > buf ? " " : "", (unsigned long long) (t / USEC_PER_SEC), (unsigned long long) (t % USEC_PER_SEC));
+        p += MIN((size_t) k, l);
+
         *p = 0;
 
         return buf;
@@ -2638,6 +2639,7 @@ int parse_usec(const char *t, usec_t *usec) {
         } table[] = {
                 { "sec", USEC_PER_SEC },
                 { "s", USEC_PER_SEC },
+                { ".", USEC_PER_SEC },
                 { "min", USEC_PER_MINUTE },
                 { "hr", USEC_PER_HOUR },
                 { "h", USEC_PER_HOUR },
@@ -2651,6 +2653,17 @@ int parse_usec(const char *t, usec_t *usec) {
                 { "", USEC_PER_SEC },
         };
 
+        static const usec_t fract[] = {
+                0LL,
+                1000000LL,
+                100000LL,
+                10000LL,
+                1000LL,
+                100LL,
+                10LL,
+                1LL
+        };
+
         const char *p;
         usec_t r = 0;
 
@@ -2658,6 +2671,7 @@ int parse_usec(const char *t, usec_t *usec) {
         assert(usec);
 
         p = t;
+        char *seen_p = NULL;
         do {
                 long long l;
                 char *e;
@@ -2679,7 +2693,13 @@ int parse_usec(const char *t, usec_t *usec) {
 
                 for (i = 0; i < ELEMENTSOF(table); i++)
                         if (startswith(e, table[i].suffix)) {
-                                r += (usec_t) l * table[i].usec;
+                                if (seen_p) {
+                                        if (*e != 's' || e - seen_p >= sizeof fract / sizeof fract[0])
+                                                return -EINVAL;
+                                        r += (usec_t) l * fract[e - seen_p];
+                                } else
+                                        r += (usec_t) l * table[i].usec;
+                                seen_p = table[i].suffix[0] == '.'? e: NULL;
                                 p = e + strlen(table[i].suffix);
                                 break;
                         }