diff --git a/src/humanize/time.py b/src/humanize/time.py
index 3fbefed..07cda8a 100644
--- a/src/humanize/time.py
+++ b/src/humanize/time.py
@@ -39,6 +39,20 @@ def __lt__(self, other):
             return self.value < other.value
         return NotImplemented
 
+    def succ(self):
+        if self == Unit.YEARS:
+            raise IndexError()
+
+        v = self.value + 1
+        return Unit(v)
+
+    def pred(self):
+        if self == Unit.MICROSECONDS:
+            raise IndexError()
+
+        v = self.value - 1
+        return Unit(v)
+
 
 def _now():
     return dt.datetime.now()
@@ -396,7 +410,9 @@ def _suppress_lower_units(min_unit, suppress):
     return suppress
 
 
-def precisedelta(value, minimum_unit="seconds", suppress=(), format="%0.2f") -> str:
+def precisedelta(
+    value, minimum_unit="seconds", suppress=(), format="%0.2f", truncate=False
+) -> str:
     """Return a precise representation of a timedelta.
 
     ```pycon
@@ -503,12 +519,8 @@ def precisedelta(value, minimum_unit="seconds", suppress=(), format="%0.2f") ->
     years, days = _quotient_and_remainder(days, 365, YEARS, min_unit, suppress)
     months, days = _quotient_and_remainder(days, 30.5, MONTHS, min_unit, suppress)
 
-    # If DAYS is not in suppress, we can represent the days but
-    # if it is a suppressed unit, we need to carry it to a lower unit,
-    # seconds in this case.
-    #
-    # The same applies for secs and usecs below
-    days, secs = _carry(days, secs, 24 * 3600, DAYS, min_unit, suppress)
+    secs = days * 24 * 3600 + secs
+    days, secs = _quotient_and_remainder(secs, 24 * 3600, DAYS, min_unit, suppress)
 
     hours, secs = _quotient_and_remainder(secs, 3600, HOURS, min_unit, suppress)
     minutes, secs = _quotient_and_remainder(secs, 60, MINUTES, min_unit, suppress)
@@ -533,6 +545,14 @@ def precisedelta(value, minimum_unit="seconds", suppress=(), format="%0.2f") ->
         ("%d microsecond", "%d microseconds", usecs),
     ]
 
+    if truncate:
+        for unit, fmt in reversed(list(zip(reversed(Unit), fmts))):
+            _x, _x, value = fmt
+            if unit == min_unit:
+                value = int(value)
+                if value == 0 and min_unit < YEARS:
+                    min_unit = min_unit.succ()
+
     texts = []
     for unit, fmt in zip(reversed(Unit), fmts):
         singular_txt, plural_txt, value = fmt
diff --git a/tests/issue-14-days-hours-boundary-in-precisedelta.md b/tests/issue-14-days-hours-boundary-in-precisedelta.md
new file mode 100755
index 0000000..ea0a3cb
--- /dev/null
+++ b/tests/issue-14-days-hours-boundary-in-precisedelta.md
@@ -0,0 +1,94 @@
+# Days / hours boundary in `precisedelta`
+
+When a `timedelta` is described by `precisedelta`, it
+is aimed to be as human as possible.
+
+```python
+>>> import humanize
+>>> import datetime
+
+>>> humanize.precisedelta(datetime.timedelta(days=31))
+'1 month and 12 hours'
+
+>>> humanize.precisedelta(datetime.timedelta(days=62))
+'2 months and 1 day'
+
+>>> humanize.precisedelta(datetime.timedelta(days=92))
+'3 months and 12 hours'
+
+>>> humanize.precisedelta(datetime.timedelta(days=32))
+'1 month, 1 day and 12 hours'
+```
+
+Setting a minimum unit forces us to use fractional value for the latest
+unit, in this case, `days`:
+
+```python
+>>> humanize.precisedelta(datetime.timedelta(days=31), minimum_unit='days')
+'1 month and 0.50 days'
+
+>>> humanize.precisedelta(datetime.timedelta(days=62), minimum_unit='days')
+'2 months and 1 day'
+
+>>> humanize.precisedelta(datetime.timedelta(days=92), minimum_unit='days')
+'3 months and 0.50 days'
+
+>>> humanize.precisedelta(datetime.timedelta(days=32), minimum_unit='days')
+'1 month and 1.50 days'
+```
+
+The `format` controls how this fractional (latest) value is formatted.
+Using an integer representation like `'%d'` may yield unexpected results
+as things like `0.50 days` are cast to `0 days` during the formatting:
+
+```python
+>>> humanize.precisedelta(datetime.timedelta(days=31), minimum_unit='days', format='%d')
+'1 month and 0 days'
+
+>>> humanize.precisedelta(datetime.timedelta(days=62), minimum_unit='days', format='%d')
+'2 months and 1 day'
+
+>>> humanize.precisedelta(datetime.timedelta(days=92), minimum_unit='days', format='%d')
+'3 months and 0 days'
+
+>>> humanize.precisedelta(datetime.timedelta(days=32), minimum_unit='days', format='%d')
+'1 month and 1 days'
+```
+
+`precisedelta` accepts a `truncate` flag to truncate and drop values too
+close to zero.
+
+```python
+>>> humanize.precisedelta(datetime.timedelta(days=31), minimum_unit='days', format='%d', truncate=True)
+'1 month'
+
+>>> humanize.precisedelta(datetime.timedelta(days=62), minimum_unit='days', format='%d', truncate=True)
+'2 months and 1 day'
+
+>>> humanize.precisedelta(datetime.timedelta(days=92), minimum_unit='days', format='%d', truncate=True)
+'3 months'
+
+>>> humanize.precisedelta(datetime.timedelta(days=32), minimum_unit='days', format='%d', truncate=True)
+'1 month and 1 days'
+```
+
+Notice the `truncate=True` does not imply `format='%d'` as fractional
+numbers are still possible and `format` still apply:
+
+```python
+>>> humanize.precisedelta(datetime.timedelta(days=31), minimum_unit='days', truncate=True)
+'1 month'
+
+>>> humanize.precisedelta(datetime.timedelta(days=62), minimum_unit='days', truncate=True)
+'2 months and 1 day'
+
+>>> humanize.precisedelta(datetime.timedelta(days=92), minimum_unit='days', truncate=True)
+'3 months'
+
+>>> humanize.precisedelta(datetime.timedelta(days=32), minimum_unit='days', truncate=True)
+'1 month and 1.50 days'
+```
+
+## References
+
+See [issue 14](https://github.com/python-humanize/humanize/issues/14)