diff --git a/src/cmd/compile/internal/gc/esc.go b/src/cmd/compile/internal/gc/esc.go
index 322b2dcd0b..bd0fb82554 100644
--- a/src/cmd/compile/internal/gc/esc.go
+++ b/src/cmd/compile/internal/gc/esc.go
@@ -2105,6 +2105,16 @@ func (e *EscState) escwalkBody(level Level, dst *Node, src *Node, step *EscStep,
 				step.describe(src)
 			}
 			extraloopdepth = modSrcLoopdepth
+			if src.Op == OCONVIFACE {
+				lt := src.Left.Type
+				if !lt.IsInterface() && !isdirectiface(lt) && types.Haspointers(lt) {
+					// We're converting from a non-direct interface type.
+					// The interface will hold a heap copy of the data
+					// (by calling convT2I or friend). Flow the data to heap.
+					// See issue 29353.
+					e.escwalk(level, &e.theSink, src.Left, e.stepWalk(dst, src.Left, "interface-converted", step))
+				}
+			}
 		}
 
 	case ODOT,
diff --git a/test/escape_because.go b/test/escape_because.go
index 3b67ff9e4b..64fa28ddda 100644
--- a/test/escape_because.go
+++ b/test/escape_because.go
@@ -43,7 +43,7 @@ func f2(q *int) { // ERROR "from &u \(address-of\) at escape_because.go:43$" "fr
 	sink = &u // ERROR "&u escapes to heap$" "from &u \(interface-converted\) at escape_because.go:43$" "from sink \(assigned to top level variable\) at escape_because.go:43$"
 }
 
-func f3(r *int) interface{} { // ERROR "from \[\]\*int literal \(slice-literal-element\) at escape_because.go:47$" "from c \(assigned\) at escape_because.go:47$" "from c \(interface-converted\) at escape_because.go:48$" "from ~r1 \(return\) at escape_because.go:48$" "leaking param: r to result ~r1 level=-1$"
+func f3(r *int) interface{} { // ERROR "from \[\]\*int literal \(slice-literal-element\) at escape_because.go:47$" "from c \(assigned\) at escape_because.go:47$" "from c \(interface-converted\) at escape_because.go:48$" "from ~r1 \(return\) at escape_because.go:48$" "leaking param: r"
 	c := []*int{r} // ERROR "\[\]\*int literal escapes to heap$" "from c \(assigned\) at escape_because.go:47$" "from c \(interface-converted\) at escape_because.go:48$" "from ~r1 \(return\) at escape_because.go:48$"
 	return c       // "return" // ERROR "c escapes to heap$" "from ~r1 \(return\) at escape_because.go:48$"
 }
diff --git a/test/escape_param.go b/test/escape_param.go
index dff13b6f7c..175a4f03dd 100644
--- a/test/escape_param.go
+++ b/test/escape_param.go
@@ -424,3 +424,18 @@ func h(x *Node) { // ERROR "leaking param: x"
 	Sink = g(y)
 	f(y)
 }
+
+// interface(in) -> out
+// See also issue 29353.
+
+// Convert to a non-direct interface, require an allocation and
+// copy x to heap (not to result).
+func param14a(x [4]*int) interface{} { // ERROR "leaking param: x$"
+	return x // ERROR "x escapes to heap"
+}
+
+// Convert to a direct interface, does not need an allocation.
+// So x only leaks to result.
+func param14b(x *int) interface{} { // ERROR "leaking param: x to result ~r1 level=0"
+	return x // ERROR "x escapes to heap"
+}