diff --git a/python/cudf/cudf/_lib/column.pyx b/python/cudf/cudf/_lib/column.pyx
index 7155017b7af..e030147fdd3 100644
--- a/python/cudf/cudf/_lib/column.pyx
+++ b/python/cudf/cudf/_lib/column.pyx
@@ -202,11 +202,13 @@ cdef class Column:
 
     def _clear_cache(self):
         self._distinct_count = {}
-        try:
-            del self.memory_usage
-        except AttributeError:
-            # `self.memory_usage` was never called before, So ignore.
-            pass
+        attrs = ("memory_usage", "is_monotonic_increasing", "is_monotonic_decreasing")
+        for attr in attrs:
+            try:
+                delattr(self, attr)
+            except AttributeError:
+                # attr was not called yet, so ignore.
+                pass
         self._null_count = None
 
     def set_mask(self, value):
diff --git a/python/cudf/cudf/core/column/column.py b/python/cudf/cudf/core/column/column.py
index dbdf501e022..9467bbeed15 100644
--- a/python/cudf/cudf/core/column/column.py
+++ b/python/cudf/cudf/core/column/column.py
@@ -274,7 +274,10 @@ def any(self, skipna: bool = True) -> bool:
         return libcudf.reduce.reduce("any", self, dtype=np.bool_)
 
     def dropna(self) -> Self:
-        return drop_nulls([self])[0]._with_type_metadata(self.dtype)
+        if self.has_nulls():
+            return drop_nulls([self])[0]._with_type_metadata(self.dtype)
+        else:
+            return self.copy()
 
     def to_arrow(self) -> pa.Array:
         """Convert to PyArrow Array
@@ -699,6 +702,9 @@ def fillna(
 
     def isnull(self) -> ColumnBase:
         """Identify missing values in a Column."""
+        if not self.has_nulls(include_nan=self.dtype.kind == "f"):
+            return as_column(False, length=len(self))
+
         result = libcudf.unary.is_null(self)
 
         if self.dtype.kind == "f":
@@ -710,6 +716,9 @@ def isnull(self) -> ColumnBase:
 
     def notnull(self) -> ColumnBase:
         """Identify non-missing values in a Column."""
+        if not self.has_nulls(include_nan=self.dtype.kind == "f"):
+            return as_column(True, length=len(self))
+
         result = libcudf.unary.is_valid(self)
 
         if self.dtype.kind == "f":
@@ -922,15 +931,16 @@ def as_mask(self) -> Buffer:
 
     @property
     def is_unique(self) -> bool:
+        # distinct_count might already be cached
         return self.distinct_count(dropna=False) == len(self)
 
-    @property
+    @cached_property
     def is_monotonic_increasing(self) -> bool:
         return not self.has_nulls(include_nan=True) and libcudf.sort.is_sorted(
             [self], [True], None
         )
 
-    @property
+    @cached_property
     def is_monotonic_decreasing(self) -> bool:
         return not self.has_nulls(include_nan=True) and libcudf.sort.is_sorted(
             [self], [False], None
@@ -941,6 +951,10 @@ def sort_values(
         ascending: bool = True,
         na_position: str = "last",
     ) -> ColumnBase:
+        if (not ascending and self.is_monotonic_decreasing) or (
+            ascending and self.is_monotonic_increasing
+        ):
+            return self.copy()
         return libcudf.sort.sort(
             [self], column_order=[ascending], null_precedence=[na_position]
         )[0]
@@ -1090,11 +1104,22 @@ def apply_boolean_mask(self, mask) -> ColumnBase:
         )
 
     def argsort(
-        self, ascending: bool = True, na_position: str = "last"
-    ) -> "cudf.core.column.NumericalColumn":
-        return libcudf.sort.order_by(
-            [self], [ascending], na_position, stable=True
-        )
+        self,
+        ascending: bool = True,
+        na_position: Literal["first", "last"] = "last",
+    ) -> cudf.core.column.NumericalColumn:
+        if (ascending and self.is_monotonic_increasing) or (
+            not ascending and self.is_monotonic_decreasing
+        ):
+            return as_column(range(len(self)))
+        elif (ascending and self.is_monotonic_decreasing) or (
+            not ascending and self.is_monotonic_increasing
+        ):
+            return as_column(range(len(self) - 1, -1, -1))
+        else:
+            return libcudf.sort.order_by(
+                [self], [ascending], na_position, stable=True
+            )
 
     def __arrow_array__(self, type=None):
         raise TypeError(
@@ -1157,9 +1182,12 @@ def unique(self) -> ColumnBase:
         """
         Get unique values in the data
         """
-        return drop_duplicates([self], keep="first")[0]._with_type_metadata(
-            self.dtype
-        )
+        if self.is_unique:
+            return self.copy()
+        else:
+            return drop_duplicates([self], keep="first")[
+                0
+            ]._with_type_metadata(self.dtype)
 
     def serialize(self) -> tuple[dict, list]:
         # data model: