diff --git a/src/Simplify.cpp b/src/Simplify.cpp
index 6bb34fc4db15..284eaa76568d 100644
--- a/src/Simplify.cpp
+++ b/src/Simplify.cpp
@@ -276,6 +276,24 @@ void Simplify::ScopedFact::learn_true(const Expr &fact) {
                 learn_lower_bound(v, i.bounds.min + 1);
             }
         }
+        const Min *min = lt->b.as<Min>();
+        if (min) {
+            // c < min(a, b) -> c < a, c < b
+            learn_true(lt->a < min->a);
+            learn_true(lt->a < min->b);
+            // c < min(a, b) -> !(a <= c), !(b <= c)
+            learn_false(min->a <= lt->a);
+            learn_false(min->b <= lt->a);
+        }
+        const Max *max = lt->a.as<Max>();
+        if (max) {
+            // max(a, b) < c -> a < c, b < c
+            learn_true(max->a < lt->b);
+            learn_true(max->b < lt->b);
+            // max(a, b) < c -> !(c <= a), !(c <= b)
+            learn_false(lt->b <= max->a);
+            learn_false(lt->b <= max->b);
+        }
     } else if (const LE *le = fact.as<LE>()) {
         const Variable *v = le->a.as<Variable>();
         Simplify::ExprInfo i;
@@ -294,6 +312,24 @@ void Simplify::ScopedFact::learn_true(const Expr &fact) {
                 learn_lower_bound(v, i.bounds.min);
             }
         }
+        const Min *min = le->b.as<Min>();
+        if (min) {
+            // c <= min(a, b) -> c <= a, c <= b
+            learn_true(le->a <= min->a);
+            learn_true(le->a <= min->b);
+            // c <= min(a, b) -> !(a < c), !(b < c)
+            learn_false(min->a < le->a);
+            learn_false(min->b < le->a);
+        }
+        const Max *max = le->a.as<Max>();
+        if (max) {
+            // max(a, b) <= c -> a <= c, b <= c
+            learn_true(max->a <= le->b);
+            learn_true(max->b <= le->b);
+            // max(a, b) <= c -> !(c < a), !(c < b)
+            learn_false(le->b < max->a);
+            learn_false(le->b < max->b);
+        }
     } else if (const Call *c = Call::as_tag(fact)) {
         learn_true(c->args[0]);
         return;
diff --git a/test/correctness/CMakeLists.txt b/test/correctness/CMakeLists.txt
index 8ca5cfb05045..d3ca7ead1586 100644
--- a/test/correctness/CMakeLists.txt
+++ b/test/correctness/CMakeLists.txt
@@ -296,6 +296,7 @@ tests(GROUPS correctness
       sort_exprs.cpp
       specialize.cpp
       specialize_to_gpu.cpp
+      specialize_trim_condition.cpp
       split_by_non_factor.cpp
       split_fuse_rvar.cpp
       split_reuse_inner_name_bug.cpp
diff --git a/test/correctness/specialize_trim_condition.cpp b/test/correctness/specialize_trim_condition.cpp
new file mode 100644
index 000000000000..c2753e17c09f
--- /dev/null
+++ b/test/correctness/specialize_trim_condition.cpp
@@ -0,0 +1,78 @@
+#include "Halide.h"
+#include "HalideRuntime.h"
+#include <assert.h>
+#include <stdio.h>
+#include <stdlib.h>
+
+using namespace Halide;
+
+int load_count = 0;
+
+// A trace that records the number of loads
+int my_trace(JITUserContext *user_context, const halide_trace_event_t *ev) {
+
+    if (ev->event == halide_trace_load) {
+        load_count++;
+    }
+    return 0;
+}
+
+int main(int argc, char **argv) {
+    Param<float> scale_factor_x, scale_factor_y;
+    ImageParam input(UInt(8), 2);
+
+    Var x, y;
+
+    Func f;
+    Expr upsample_x = scale_factor_x > cast<float>(1.0f);
+    Expr upsample_y = scale_factor_y > cast<float>(1.0f);
+    Expr upsample = upsample_x && upsample_y;
+    Expr downsample = !upsample_x && !upsample_y;
+
+    f(x, y) = select(upsample, input(cast<int>(x / 2), cast<int>(y / 2)),
+                     select(downsample, input(x * 2, y * 2), 0));
+
+    input.trace_loads();
+    f.jit_handlers().custom_trace = &my_trace;
+
+    // Impossible condition
+    // f.specialize(upsample && downsample);
+    f.specialize(upsample && !downsample);
+    f.specialize(!upsample && downsample);
+    f.specialize(!upsample && !downsample);
+    f.specialize_fail("Unreachable condition");
+
+    Buffer<uint8_t> img(16, 16);
+    input.set(img);
+
+    {
+        // In this specialization, one of the select branches should be trimmed,
+        // resulting in one load per output pixel
+        load_count = 0;
+        scale_factor_x.set(2.0f);
+        scale_factor_y.set(2.0f);
+        Buffer<uint8_t> out = f.realize({8, 8});
+        assert(load_count == 64);
+    }
+    {
+        // In this specialization, no select can be trimmed,
+        // resulting in two loads per output pixel
+        load_count = 0;
+        scale_factor_x.set(0.5f);
+        scale_factor_y.set(2.0f);
+        Buffer<uint8_t> out = f.realize({8, 8});
+        assert(load_count == 128);
+    }
+    {
+        // In this specialization, one of the select branches should be trimmed,
+        // resulting in one load per output pixel
+        load_count = 0;
+        scale_factor_x.set(0.5f);
+        scale_factor_y.set(0.5f);
+        Buffer<uint8_t> out = f.realize({8, 8});
+        assert(load_count == 64);
+    }
+
+    printf("Success!\n");
+    return 0;
+}