diff --git a/src/Lean/Compiler/LCNF/ToLCNF.lean b/src/Lean/Compiler/LCNF/ToLCNF.lean
index 096c207e31..e329139247 100644
--- a/src/Lean/Compiler/LCNF/ToLCNF.lean
+++ b/src/Lean/Compiler/LCNF/ToLCNF.lean
@@ -529,30 +529,37 @@ where
         let typeName := casesInfo.declName.getPrefix
         let discr ← visitAppArg args[casesInfo.discrPos]!
         let .inductInfo indVal ← getConstInfo typeName | unreachable!
-        for i in casesInfo.altsRange, numParams in casesInfo.altNumParams, ctorName in indVal.ctors do
-          let (altType, alt) ← visitAlt ctorName numParams args[i]!
-          unless (← compatibleTypes altType resultType) do
-            resultType := anyTypeExpr
-          alts := alts.push alt
-        if resultType.isAnyType || resultType.isErased then
+        if !discr.isFVar then
           /-
-          If the result type for a `cases` is `⊤` or `◾`, we put a cast to `⊤`
-          at every alternative that does not have `⊤` type.
-          The cast is useful to ensure the result is type correct when reducing `cases` in the simplifier
-          or applying `bind`. For example, suppose we are using `Code.bind` to connect a `cases` with type `⊤`
-          to a continuation that expects type `B`, and one of the alternatives has type `A`. The operation makes
-          sense, but we need a cast since we are connecting a value of type `A` to a continuation that expects `B`.
+          This can happen for inductive predicates that can eliminate into type (e.g., `And`, `Iff`).
+          TODO: add support for them. Right now, we have hard-coded support for the ones defined at `Init`.
           -/
-          alts ← alts.mapM fun alt =>
-            return alt.updateCode (← alt.getCode.ensureAnyType)
-        let cases : Cases := { typeName, discr := discr.fvarId!, resultType, alts }
-        let auxDecl ← mkAuxParam resultType
-        pushElement (.cases auxDecl cases)
-        let result := .fvar auxDecl.fvarId
-        if args.size == casesInfo.arity then
-          return result
+          throwError "unsupported `{casesInfo.declName}` application during code generation"
         else
-          mkOverApplication result args casesInfo.arity
+          for i in casesInfo.altsRange, numParams in casesInfo.altNumParams, ctorName in indVal.ctors do
+            let (altType, alt) ← visitAlt ctorName numParams args[i]!
+            unless (← compatibleTypes altType resultType) do
+              resultType := anyTypeExpr
+            alts := alts.push alt
+          if resultType.isAnyType || resultType.isErased then
+            /-
+            If the result type for a `cases` is `⊤` or `◾`, we put a cast to `⊤`
+            at every alternative that does not have `⊤` type.
+            The cast is useful to ensure the result is type correct when reducing `cases` in the simplifier
+            or applying `bind`. For example, suppose we are using `Code.bind` to connect a `cases` with type `⊤`
+            to a continuation that expects type `B`, and one of the alternatives has type `A`. The operation makes
+            sense, but we need a cast since we are connecting a value of type `A` to a continuation that expects `B`.
+            -/
+            alts ← alts.mapM fun alt =>
+              return alt.updateCode (← alt.getCode.ensureAnyType)
+          let cases : Cases := { typeName, discr := discr.fvarId!, resultType, alts }
+          let auxDecl ← mkAuxParam resultType
+          pushElement (.cases auxDecl cases)
+          let result := .fvar auxDecl.fvarId
+          if args.size == casesInfo.arity then
+            return result
+          else
+            mkOverApplication result args casesInfo.arity
 
   visitCtor (arity : Nat) (e : Expr) : M Expr :=
     etaIfUnderApplied e arity do
@@ -594,13 +601,13 @@ where
       let type ← toLCNFType (← liftMetaM do Meta.inferType e)
       mkUnreachable type
 
-  visitAndRec (e : Expr) : M Expr :=
+  visitAndIffRecCore (e : Expr) (minorPos : Nat) : M Expr :=
     let arity := 5
     etaIfUnderApplied e arity do
       let args := e.getAppArgs
       let ha := mkLcProof args[0]! -- We should not use `lcErased` here since we use it to create a pre-LCNF Expr.
       let hb := mkLcProof args[1]!
-      let minor := if e.isAppOf ``And.rec then args[3]! else args[4]!
+      let minor := args[minorPos]!
       let minor := minor.beta #[ha, hb]
       visit (mkAppN minor args[arity:])
 
@@ -661,8 +668,10 @@ where
         visitCtor 3 e
       else if declName == ``Eq.casesOn || declName == ``Eq.rec || declName == ``Eq.ndrec then
         visitEqRec e
-      else if declName == ``And.rec || declName == ``And.casesOn then
-        visitAndRec e
+      else if declName == ``And.rec || declName == ``Iff.rec then
+        visitAndIffRecCore e (minorPos := 3)
+      else if declName == ``And.casesOn || declName == ``Iff.casesOn then
+        visitAndIffRecCore e (minorPos := 4)
       else if declName == ``False.rec || declName == ``Empty.rec || declName == ``False.casesOn || declName == ``Empty.casesOn then
         visitFalseRec e
       else if let some casesInfo ← getCasesInfo? declName then
diff --git a/tests/lean/run/1684.lean b/tests/lean/run/1684.lean
new file mode 100644
index 0000000000..7cf51fb171
--- /dev/null
+++ b/tests/lean/run/1684.lean
@@ -0,0 +1,7 @@
+set_option trace.Compiler.result true
+
+def Iff.elim1.{u} {a b : Prop} {motive : Sort u} (t : a ↔ b) (h : (mp : a → b) → (mpr : b → a) → motive) : motive :=
+  match t with | ⟨hab, hba⟩ => h hab hba
+
+def Iff.elim2.{u} {a b : Prop} {motive : Sort u} (t : a ↔ b) (h : (mp : a → b) → (mpr : b → a) → motive) : motive :=
+  Iff.casesOn (motive:= fun _ : a ↔ b => motive) t h