diff --git a/src/operators.jl b/src/operators.jl
index d8f0ec9..f4cf299 100644
--- a/src/operators.jl
+++ b/src/operators.jl
@@ -19,6 +19,40 @@ for f in (
 end
 
 # Implement the binary operators: +, -, *, /, %, &, |, ^, <<, and >>
+# Prevent ambiguities with Base
+@inline function Base.(:^){S1, S2<:Integer}(x::Nullable{S1}, y::S2)
+    if isbits(S1) & isbits(S2)
+        Nullable(^(x.value, y), x.isnull)
+    else
+        throw_error()
+    end
+end
+
+for f in (
+    :(Base.(:<<)),
+    :(Base.(:>>))
+)
+    @eval begin
+        @inline function $(f){S1}(x::Nullable{S1}, y::Int)
+            if isbits(S1)
+                Nullable($(f)(x.value, y), x.isnull)
+            else
+                throw_error()
+            end
+        end
+    end
+
+    @eval begin
+        @inline function $(f){S1, T<:Integer}(x::Nullable{S1}, y::T)
+            if isbits(S1) && isbits(T)
+                Nullable($(f)(x.value, y), x.isnull)
+            else
+                throw_error()
+            end
+        end
+    end
+end
+
 for f in (
     :(Base.(:+)),
     :(Base.(:-)),
@@ -40,24 +74,38 @@ for f in (
             end
         end
     end
-end
 
-# Implement the binary operators: == and !=
-for f in (
-    :(Base.(:(==))),
-    :(Base.(:!=)),
-)
     @eval begin
-        function $(f){S1, S2}(x::Nullable{S1}, y::Nullable{S2})
+        @inline function $(f){S1, S2}(x::Nullable{S1}, y::S2)
             if isbits(S1) & isbits(S2)
-                Nullable{Bool}($(f)(x.value, y.value), x.isnull | y.isnull)
+                Nullable($(f)(x.value, y), x.isnull)
             else
-                error()
+                throw_error()
             end
         end
     end
 end
 
+# Implement the binary operators: == and !=
+# Prevent ambiguity with Base
+Base.(:(==))(x::Nullable, y::WeakRef) = x == y.value
+
+function Base.(:(==)){S1, S2}(x::Nullable{S1}, y::Nullable{S2})
+    if isbits(S1) & isbits(S2)
+        Nullable{Bool}(x.value == y.value, x.isnull | y.isnull)
+    else
+        error()
+    end
+end
+
+function Base.(:(==)){S1, S2}(x::Nullable{S1}, y::S2)
+    if isbits(S1) & isbits(S2)
+        Nullable{Bool}(x.value == y, x.isnull)
+    else
+        error()
+    end
+end
+
 # Implement the binary operators: <, >, <=, and >=
 for f in (
     :(Base.(:<)),
@@ -74,6 +122,16 @@ for f in (
             end
         end
     end
+
+    @eval begin
+        function $(f){S1, S2}(x::Nullable{S1}, y::S2)
+            if isbits(S1) & isbits(S2)
+                Nullable{Bool}($(f)(x.value, y), x.isnull)
+            else
+                error()
+            end
+        end
+    end
 end
 
 # Miscellaneous lifted operators
@@ -112,6 +170,14 @@ function Base.call{S1, S2}(::Base.MinFun, x::Nullable{S1}, y::Nullable{S2})
     end
 end
 
+function Base.call{S1, S2}(::Base.MinFun, x::Nullable{S1}, y::Nullable{S2})
+    if isbits(S1) & isbits(S2)
+        return Nullable(Base.scalarmin(x.value, y.value), x.isnull | y.isnull)
+    else
+        error()
+    end
+end
+
 function Base.call{S1, S2}(::Base.MaxFun, x::Nullable{S1}, y::Nullable{S2})
     if isbits(S1) & isbits(S2)
         return Nullable(Base.scalarmax(x.value, y.value), x.isnull | y.isnull)
diff --git a/test/operators.jl b/test/operators.jl
index 127fa1b..bd96edd 100644
--- a/test/operators.jl
+++ b/test/operators.jl
@@ -46,6 +46,9 @@ module TestOperators
         x = op(Nullable(v), Nullable(w))
         @test_approx_eq x.value op(v, w)
         @test !x.isnull
+        y = op(Nullable(v), w)
+        @test_approx_eq y.value op(v, w)
+        @test !y.isnull
         @test_throws ErrorException op(Nullable(rand(1)), Nullable(rand(1)))
     end
 
@@ -58,6 +61,9 @@ module TestOperators
         x = op(Nullable(v), Nullable(w))
         @test_approx_eq x.value op(v, w)
         @test !x.isnull
+        y = op(Nullable(v), w)
+        @test_approx_eq y.value op(v, w)
+        @test !y.isnull
         @test_throws ErrorException op(Nullable(rand(Bool, 1)), Nullable(rand(Bool, 1)))
     end
 
@@ -70,6 +76,9 @@ module TestOperators
         x = op(Nullable(v), Nullable(w))
         @test_approx_eq x.value op(v, w)
         @test !x.isnull
+        y = op(Nullable(v), w)
+        @test_approx_eq y.value op(v, w)
+        @test !y.isnull
         @test_throws ErrorException op(Nullable(rand(Int, 1)), Nullable(rand(Int, 1)))
     end
 end