diff --git a/lib/circular_buffer.ex b/lib/circular_buffer.ex
index e2a6ec3..152602f 100644
--- a/lib/circular_buffer.ex
+++ b/lib/circular_buffer.ex
@@ -34,7 +34,7 @@ defmodule CircularBuffer do
   @opaque t() :: %__MODULE__{
             a: list(),
             b: list(),
-            max_size: pos_integer(),
+            max_size: non_neg_integer(),
             count: non_neg_integer()
           }
 
@@ -43,8 +43,8 @@ defmodule CircularBuffer do
   @doc """
   Creates a new circular buffer with a given size.
   """
-  @spec new(pos_integer()) :: t()
-  def new(size) when is_integer(size) and size > 0 do
+  @spec new(non_neg_integer()) :: t()
+  def new(size) when is_integer(size) and size >= 0 do
     %CB{a: [], b: [], max_size: size, count: 0}
   end
 
@@ -60,11 +60,14 @@ defmodule CircularBuffer do
     %{cb | a: [item | cb.a], count: cb.count + 1}
   end
 
-  def insert(%CB{b: []} = cb, item) do
-    new_b = cb.a |> Enum.reverse() |> tl()
+  def insert(%CB{a: a, b: []} = cb, item) when a != [] do
+    new_b = a |> Enum.reverse() |> tl()
     %{cb | a: [item], b: new_b}
   end
 
+  # max_size==0 case
+  def insert(cb, _item), do: cb
+
   @doc """
   Converts a circular buffer to a list. The list is ordered from oldest to newest
   elements based on their insertion order.
diff --git a/test/circular_buffer_test.exs b/test/circular_buffer_test.exs
index 4fb3871..9f01299 100644
--- a/test/circular_buffer_test.exs
+++ b/test/circular_buffer_test.exs
@@ -11,8 +11,8 @@ defmodule CircularBufferTest do
 
   alias CircularBuffer, as: CB
 
-  property "new/1 returns an empty buffer for positive sizes" do
-    forall size <- pos_integer() do
+  property "new/1 returns an empty buffer for non-negative sizes" do
+    forall size <- non_neg_integer() do
       cb = CB.new(size)
 
       cb.max_size == size and
@@ -23,10 +23,10 @@ defmodule CircularBufferTest do
     end
   end
 
-  property "new/1 raises for non-positive sizes" do
-    forall n <- non_neg_integer() do
+  property "new/1 raises for negative sizes" do
+    forall n <- neg_integer() do
       try do
-        CB.new(-n)
+        CB.new(n)
         false
       rescue
         FunctionClauseError -> true
@@ -39,14 +39,14 @@ defmodule CircularBufferTest do
   end
 
   property "the count matches the number of elements in the buffer" do
-    forall {size, is} <- {pos_integer(), list(integer())} do
+    forall {size, is} <- {non_neg_integer(), list(integer())} do
       buffer = Enum.reduce(is, CB.new(size), fn i, cb -> CB.insert(cb, i) end)
       slow_cb_count(buffer) == buffer.count
     end
   end
 
   property "can tell the current number of elements" do
-    forall {size, is} <- {pos_integer(), list(integer())} do
+    forall {size, is} <- {non_neg_integer(), list(integer())} do
       buffer = Enum.reduce(is, CB.new(size), fn i, cb -> CB.insert(cb, i) end)
       Enum.count(buffer) == min(size, length(is))
     end