diff --git a/flox/core.py b/flox/core.py
index d1ac8815..633bd695 100644
--- a/flox/core.py
+++ b/flox/core.py
@@ -179,7 +179,9 @@ def _is_minmax_reduction(func: T_Agg) -> bool:
 
 
 def _is_first_last_reduction(func: T_Agg) -> bool:
-    return isinstance(func, str) and func in ["nanfirst", "nanlast", "first", "last"]
+    if isinstance(func, Aggregation):
+        func = func.name
+    return func in ["nanfirst", "nanlast", "first", "last"]
 
 
 def _get_expected_groups(by: T_By, sort: bool) -> T_ExpectIndex:
@@ -680,6 +682,7 @@ def rechunk_for_blockwise(
             abs(max(newchunks) - max(chunks)) / max(chunks) < BLOCKWISE_RECHUNK_CHUNK_SIZE_THRESHOLD
         )
     ):
+        logger.debug("Rechunking to enable blockwise.")
         # Less than 25% change in number of chunks, let's do it
         return array.rechunk({axis: newchunks})
     else:
@@ -1668,7 +1671,12 @@ def dask_groupby_agg(
     #       This allows us to discover groups at compute time, support argreductions, lower intermediate
     #       memory usage (but method="cohorts" would also work to reduce memory in some cases)
     labels_are_unknown = is_duck_dask_array(by_input) and expected_groups is None
-    do_simple_combine = not _is_arg_reduction(agg) and not labels_are_unknown
+    do_grouped_combine = (
+        _is_arg_reduction(agg)
+        or labels_are_unknown
+        or (_is_first_last_reduction(agg) and array.dtype.kind != "f")
+    )
+    do_simple_combine = not do_grouped_combine
 
     if method == "blockwise":
         #  use the "non dask" code path, but applied blockwise
@@ -2012,8 +2020,13 @@ def _validate_reindex(
     expected_groups,
     any_by_dask: bool,
     is_dask_array: bool,
+    array_dtype: Any,
 ) -> bool | None:
     # logger.debug("Entering _validate_reindex: reindex is {}".format(reindex))  # noqa
+    def first_or_last():
+        return func in ["first", "last"] or (
+            _is_first_last_reduction(func) and array_dtype.kind != "f"
+        )
 
     all_numpy = not is_dask_array and not any_by_dask
     if reindex is True and not all_numpy:
@@ -2023,7 +2036,7 @@ def _validate_reindex(
             raise ValueError(
                 "reindex=True is not a valid choice for method='blockwise' or method='cohorts'."
             )
-        if func in ["first", "last"]:
+        if first_or_last():
             raise ValueError("reindex must be None or False when func is 'first' or 'last.")
 
     if reindex is None:
@@ -2034,9 +2047,10 @@ def _validate_reindex(
         if all_numpy:
             return True
 
-        if func in ["first", "last"]:
+        if first_or_last():
             # have to do the grouped_combine since there's no good fill_value
-            reindex = False
+            # Also needed for nanfirst, nanlast with no-NaN dtypes
+            return False
 
         if method == "blockwise":
             # for grouping by dask arrays, we set reindex=True
@@ -2439,7 +2453,13 @@ def groupby_reduce(
         raise ValueError(f"method={method!r} can only be used when grouping by numpy arrays.")
 
     reindex = _validate_reindex(
-        reindex, func, method, expected_groups, any_by_dask, is_duck_dask_array(array)
+        reindex,
+        func,
+        method,
+        expected_groups,
+        any_by_dask,
+        is_duck_dask_array(array),
+        array.dtype,
     )
 
     if not is_duck_array(array):
@@ -2638,7 +2658,7 @@ def groupby_reduce(
 
         # TODO: clean this up
         reindex = _validate_reindex(
-            reindex, func, method, expected_, any_by_dask, is_duck_dask_array(array)
+            reindex, func, method, expected_, any_by_dask, is_duck_dask_array(array), array.dtype
         )
 
         if TYPE_CHECKING: