diff --git a/lib/drops/type.ex b/lib/drops/type.ex
index 840ee27..85c4030 100644
--- a/lib/drops/type.ex
+++ b/lib/drops/type.ex
@@ -246,10 +246,16 @@ defmodule Drops.Type do
         )
       end
 
-      def new(spec, constraints) when is_list(constraints) do
-        new(
-          primitive: infer_primitive(spec),
-          constraints: infer_constraints({:type, {spec, constraints}})
+      def new(predicates, opts) when is_list(opts) do
+        type = new(opts)
+        constraints =
+          case type.constraints do
+            {:and, constraints} -> {:and, constraints ++ infer_constraints(predicates)}
+            constraints when is_list(constraints) -> constraints ++ infer_constraints(predicates)
+          end
+        Elixir.Map.merge(
+          type,
+          %{constraints: constraints}
         )
       end
 
diff --git a/lib/drops/type/dsl.ex b/lib/drops/type/dsl.ex
index 58f6a44..3e52a4f 100644
--- a/lib/drops/type/dsl.ex
+++ b/lib/drops/type/dsl.ex
@@ -73,9 +73,9 @@ defmodule Drops.Type.DSL do
   """
   @doc since: "0.1.0"
 
-  @spec type({atom(), []}) :: type()
+  @spec type({atom(), list()}) :: type()
   @spec type(list: atom()) :: type()
-  @spec type(list: []) :: type()
+  @spec type(list: list()) :: type()
   @spec type([atom()]) :: [type()]
   @spec type(atom()) :: type()
 
@@ -113,8 +113,8 @@ defmodule Drops.Type.DSL do
   """
   @doc since: "0.1.0"
 
-  @spec type(atom(), []) :: type()
-  @spec type({:cast, {atom(), []}}, type()) :: type()
+  @spec type(atom(), list()) :: type()
+  @spec type({:cast, {atom(), list()}}, type()) :: type()
 
   def type([type | rest], predicates) do
     union([type | rest], predicates)
@@ -251,7 +251,7 @@ defmodule Drops.Type.DSL do
   """
   @doc since: "0.1.0"
 
-  @spec maybe(atom(), []) :: type()
+  @spec maybe(atom(), list()) :: type()
 
   def maybe(type, predicates \\ []) do
     type([nil, {type, predicates}])
@@ -289,7 +289,7 @@ defmodule Drops.Type.DSL do
   @doc since: "0.1.0"
 
   @spec string(atom()) :: type()
-  @spec string([]) :: type()
+  @spec string(list()) :: type()
 
   def string(predicate) when is_atom(predicate) do
     string([predicate])
@@ -335,7 +335,7 @@ defmodule Drops.Type.DSL do
   @doc since: "0.1.0"
 
   @spec integer(atom()) :: type()
-  @spec integer([]) :: type()
+  @spec integer(list()) :: type()
 
   def integer(predicate) when is_atom(predicate) do
     integer([predicate])
@@ -377,7 +377,7 @@ defmodule Drops.Type.DSL do
   """
   @doc since: "0.1.0"
 
-  @spec float([]) :: type()
+  @spec float(list()) :: type()
 
   def float(predicates) when is_list(predicates) do
     type(:float, predicates)
@@ -460,7 +460,7 @@ defmodule Drops.Type.DSL do
   @doc since: "0.1.0"
 
   @spec map(atom()) :: type()
-  @spec map([]) :: type()
+  @spec map(list()) :: type()
 
   def map(predicate) when is_atom(predicate) do
     map([predicate])
diff --git a/lib/drops/types/union.ex b/lib/drops/types/union.ex
index 2c49eaf..98dbc52 100644
--- a/lib/drops/types/union.ex
+++ b/lib/drops/types/union.ex
@@ -101,9 +101,27 @@ defmodule Drops.Types.Union do
         })
       end
 
+      defp constrain(%Drops.Types.Cast{input_type: input_type} = type, predicates) do
+        Map.merge(type, %{
+          input_type: constrain(input_type, predicates)
+        })
+      end
+
+      defp constrain(%Drops.Types.Union{left: left, right: right} = type, predicates) do
+        Map.merge(type, %{
+          left: constrain(left, predicates),
+          right: constrain(right, predicates)
+        })
+      end
+
       defp constrain(type, predicates) do
+        constraints =
+          case type.constraints do
+            {:and, constraints} -> {:and, constraints ++ infer_constraints(predicates)}
+            constraints when is_list(constraints) -> constraints ++ infer_constraints(predicates)
+          end
         Map.merge(type, %{
-          constraints: type.constraints ++ infer_constraints(predicates)
+          constraints: constraints
         })
       end
     end