diff --git a/Project.toml b/Project.toml
index 3c284ca23..ad96fa04e 100644
--- a/Project.toml
+++ b/Project.toml
@@ -1,6 +1,6 @@
 name = "ChainRulesCore"
 uuid = "d360d2e6-b24c-11e9-a2a3-2a2ae2dbcce4"
-version = "1.10.0"
+version = "1.10.1"
 
 [deps]
 Compat = "34da2185-b29b-5c13-b0c7-acf172513d20"
diff --git a/src/tangent_types/tangent.jl b/src/tangent_types/tangent.jl
index bb91e431e..ec7c64448 100644
--- a/src/tangent_types/tangent.jl
+++ b/src/tangent_types/tangent.jl
@@ -25,6 +25,18 @@ struct Tangent{P,T} <: AbstractTangent
     # Note: If T is a Tuple/Dict, then P is also a Tuple/Dict
     # (but potentially a different one, as it doesn't contain differentials)
     backing::T
+
+    function Tangent{P,T}(backing) where {P,T}
+        if P <: Tuple
+            T <: Tuple || _backing_error(P, T, Tuple)
+        elseif P <: AbstractDict
+            T <: AbstractDict || _backing_error(P, T, AbstractDict)
+        elseif P === Any  # can be anything
+        else  # Any other struct (including NamedTuple)
+            T <: NamedTuple || _backing_error(P, T, NamedTuple)
+        end
+        return new(backing)
+    end
 end
 
 function Tangent{P}(; kwargs...) where {P}
@@ -45,6 +57,11 @@ function Tangent{P}(d::Dict) where {P<:Dict}
     return Tangent{P,typeof(d)}(d)
 end
 
+function _backing_error(P, G, E)
+    msg = "Tangent for the primal $P should be backed by a $E type, not by $G."
+    return throw(ArgumentError(msg))
+end
+
 function Base.:(==)(a::Tangent{P,T}, b::Tangent{P,T}) where {P,T}
     return backing(a) == backing(b)
 end
diff --git a/test/tangent_types/tangent.jl b/test/tangent_types/tangent.jl
index 26e6a2422..3186aa91b 100644
--- a/test/tangent_types/tangent.jl
+++ b/test/tangent_types/tangent.jl
@@ -23,6 +23,26 @@ end
         @test typeof(Tangent{Tuple{}}()) == Tangent{Tuple{},Tuple{}}
     end
 
+    @testset "constructor" begin
+        t = (1.0, 2.0)
+        nt = (x=1, y=2.0)
+        d = Dict(:x => 1.0, :y => 2.0)
+        vals = [1, 2]
+
+        @test_throws ArgumentError Tangent{typeof(t),typeof(nt)}(nt)
+        @test_throws ArgumentError Tangent{typeof(t),typeof(d)}(d)
+
+        @test_throws ArgumentError Tangent{typeof(d),typeof(nt)}(nt)
+        @test_throws ArgumentError Tangent{typeof(d),typeof(t)}(t)
+
+        @test_throws ArgumentError Tangent{typeof(nt),typeof(vals)}(vals)
+        @test_throws ArgumentError Tangent{typeof(nt),typeof(d)}(d)
+        @test_throws ArgumentError Tangent{typeof(nt),typeof(t)}(t)
+
+        @test_throws ArgumentError Tangent{Foo,typeof(d)}(d)
+        @test_throws ArgumentError Tangent{Foo,typeof(t)}(t)
+    end
+
     @testset "==" begin
         @test Tangent{Foo}(; x=0.1, y=2.5) == Tangent{Foo}(; x=0.1, y=2.5)
         @test Tangent{Foo}(; x=0.1, y=2.5) == Tangent{Foo}(; y=2.5, x=0.1)
@@ -110,7 +130,7 @@ end
         @test_throws MethodError reverse(Tangent{Foo}(; x=1.0, y=2.0))
 
         d = Dict(:x => 1, :y => 2.0)
-        cdict = Tangent{Foo,typeof(d)}(d)
+        cdict = Tangent{typeof(d),typeof(d)}(d)
         @test_throws MethodError reverse(Tangent{Foo}())
     end