diff --git a/src/Static.jl b/src/Static.jl
index 00e4bcf..6db19a2 100644
--- a/src/Static.jl
+++ b/src/Static.jl
@@ -447,6 +447,9 @@ Base.div(::StaticNumber{X}, y::Real, m::RoundingMode) where {X} = div(X, y, m)
 Base.div(x::StaticBool, y::False) = throw(DivideError())
 Base.div(x::StaticBool, y::True) = x
 
+Base.rem(::Integer, y::One) = Zero()
+Base.rem(::Integer, y::StaticInt{-1}) = Zero()
+Base.rem(x::Zero, ::Integer) = x
 Base.rem(@nospecialize(x::StaticNumber), T::Type{<:Integer}) = rem(known(x), T)
 Base.rem(::StaticNumber{X}, ::StaticNumber{Y}) where {X, Y} = static(rem(X, Y))
 Base.rem(x::Real, ::StaticInteger{Y}) where {Y} = rem(x, Y)
@@ -485,6 +488,8 @@ Base.:(>>>)(::StaticInteger{X}, ::StaticInteger{Y}) where {X, Y} = static(>>>(X,
 Base.:(>>>)(::StaticInteger{X}, n::Integer) where {X} = >>>(X, n)
 Base.:(>>>)(x::Integer, ::StaticInteger{N}) where {N} = >>>(x, N)
 
+Base.:(&)(::Integer, y::Zero) = y
+Base.:(&)(x::Zero, ::Integer) = x
 Base.:(&)(::StaticInteger{X}, ::StaticInteger{Y}) where {X, Y} = static(X & Y)
 Base.:(&)(::StaticInteger{X}, y::Union{Integer, Missing}) where {X} = X & y
 Base.:(&)(x::Union{Integer, Missing}, ::StaticInteger{Y}) where {Y} = x & Y
diff --git a/test/runtests.jl b/test/runtests.jl
index 7f38706..7e0664e 100644
--- a/test/runtests.jl
+++ b/test/runtests.jl
@@ -111,6 +111,13 @@ end
     @test mod(static(3), static(2)) === static(1)
     @test mod(static(3), 2) == 1
     @test mod(3, static(2)) == 1
+
+    @test rem(3, static(1)) == static(0)
+    @test rem(3, static(-1)) == static(0)
+    @test rem(static(0), 3) == static(0)
+
+    @test static(0) & 3 == static(0)
+    @test 3 & static(0) == static(0)
 end
 
 @testset "StaticBool" begin