diff --git a/src/asahi/compiler/agx_compiler.h b/src/asahi/compiler/agx_compiler.h
index 348ed32d1c7..da7d51123b6 100644
--- a/src/asahi/compiler/agx_compiler.h
+++ b/src/asahi/compiler/agx_compiler.h
@@ -674,6 +674,23 @@ void agx_pack_binary(agx_context *ctx, struct util_dynarray *emission);
 
 unsigned agx_write_registers(agx_instr *I, unsigned d);
 
+struct agx_copy {
+   /* Base register destination of the copy */
+   unsigned dest;
+
+   /* Base register source of the copy */
+   unsigned src;
+
+   /* Size of the copy */
+   enum agx_size size;
+
+   /* Whether the copy has been handled. Callers must leave to false. */
+   bool done;
+};
+
+void
+agx_emit_parallel_copies(agx_builder *b, struct agx_copy *copies, unsigned n);
+
 void agx_compute_liveness(agx_context *ctx);
 void agx_liveness_ins_update(BITSET_WORD *live, agx_instr *I);
 
diff --git a/src/asahi/compiler/agx_lower_parallel_copy.c b/src/asahi/compiler/agx_lower_parallel_copy.c
new file mode 100644
index 00000000000..5211a5526ed
--- /dev/null
+++ b/src/asahi/compiler/agx_lower_parallel_copy.c
@@ -0,0 +1,283 @@
+/*
+ * Copyright (C) 2022 Alyssa Rosenzweig <alyssa@rosenzweig.io>
+ *
+ * Permission is hereby granted, free of charge, to any person obtaining a
+ * copy of this software and associated documentation files (the "Software"),
+ * to deal in the Software without restriction, including without limitation
+ * the rights to use, copy, modify, merge, publish, distribute, sublicense,
+ * and/or sell copies of the Software, and to permit persons to whom the
+ * Software is furnished to do so, subject to the following conditions:
+ *
+ * The above copyright notice and this permission notice (including the next
+ * paragraph) shall be included in all copies or substantial portions of the
+ * Software.
+ *
+ * THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
+ * IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
+ * FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT.  IN NO EVENT SHALL
+ * THE AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
+ * LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
+ * OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
+ * SOFTWARE.
+ */
+
+#include "agx_compiler.h"
+#include "agx_builder.h"
+
+/*
+ * Emits code for
+ *
+ *    for (int i = 0; i < n; ++i)
+ *       registers[dests[i]] = registers[srcs[i]];
+ *
+ * ...with all copies happening in parallel.
+ *
+ * That is, emit machine instructions equivalent to a parallel copy. This is
+ * used to lower not only parallel copies but also collects and splits, which
+ * also have parallel copy semantics.
+ *
+ * We only handles register-register copies, not general agx_index sources. This
+ * suffices for its internal use for register allocation.
+ */
+
+static void
+do_copy(agx_builder *b, const struct agx_copy *copy)
+{
+   agx_mov_to(b, agx_register(copy->dest, copy->size),
+                 agx_register(copy->src, copy->size));
+}
+
+static void
+do_swap(agx_builder *b, const struct agx_copy *copy)
+{
+   if (copy->dest == copy->src)
+      return;
+
+   agx_index x = agx_register(copy->dest, copy->size);
+   agx_index y = agx_register(copy->src, copy->size);
+
+   agx_xor_to(b, x, x, y);
+   agx_xor_to(b, y, x, y);
+   agx_xor_to(b, x, x, y);
+}
+
+struct copy_ctx {
+   /* Number of copies being processed */
+   unsigned entry_count;
+
+   /* For each physreg, the number of pending copy entries that use it as a
+    * source. Once this drops to zero, then the physreg is unblocked and can
+    * be moved to.
+    */
+   unsigned physreg_use_count[AGX_NUM_REGS];
+
+   /* For each physreg, the pending copy_entry that uses it as a dest. */
+   struct agx_copy *physreg_dest[AGX_NUM_REGS];
+
+   struct agx_copy entries[AGX_NUM_REGS];
+};
+
+static bool
+entry_blocked(struct agx_copy *entry, struct copy_ctx *ctx)
+{
+   for (unsigned i = 0; i < agx_size_align_16(entry->size); i++) {
+      if (ctx->physreg_use_count[entry->dest + i] != 0)
+         return true;
+   }
+
+   return false;
+}
+
+static bool
+is_real(struct agx_copy *entry)
+{
+   /* TODO: Allow immediates in agx_copy */
+   return true;
+}
+
+/* TODO: Generalize to other bit sizes */
+static void
+split_32bit_copy(struct copy_ctx *ctx, struct agx_copy *entry)
+{
+   assert(!entry->done);
+   assert(is_real(entry));
+   assert(agx_size_align_16(entry->size) == 2);
+   struct agx_copy *new_entry = &ctx->entries[ctx->entry_count++];
+
+   new_entry->dest = entry->dest + 1;
+   new_entry->src = entry->src + 1;
+   new_entry->done = false;
+   entry->size = AGX_SIZE_16;
+   new_entry->size = AGX_SIZE_16;
+   ctx->physreg_dest[entry->dest + 1] = new_entry;
+}
+
+void
+agx_emit_parallel_copies(agx_builder *b,
+                         struct agx_copy *copies,
+                         unsigned num_copies)
+{
+   struct copy_ctx _ctx = {
+      .entry_count = num_copies
+   };
+
+   struct copy_ctx *ctx = &_ctx;
+
+   /* Set up the bookkeeping */
+   memset(ctx->physreg_dest, 0, sizeof(ctx->physreg_dest));
+   memset(ctx->physreg_use_count, 0, sizeof(ctx->physreg_use_count));
+
+   for (unsigned i = 0; i < ctx->entry_count; i++) {
+      struct agx_copy *entry = &copies[i];
+
+      ctx->entries[i] = *entry;
+
+      for (unsigned j = 0; j < agx_size_align_16(entry->size); j++) {
+         if (is_real(entry))
+            ctx->physreg_use_count[entry->src + j]++;
+
+         /* Copies should not have overlapping destinations. */
+         assert(!ctx->physreg_dest[entry->dest + j]);
+         ctx->physreg_dest[entry->dest + j] = entry;
+      }
+   }
+
+   bool progress = true;
+   while (progress) {
+      progress = false;
+
+      /* Step 1: resolve paths in the transfer graph. This means finding
+       * copies whose destination aren't blocked by something else and then
+       * emitting them, continuing this process until every copy is blocked
+       * and there are only cycles left.
+       *
+       * TODO: We should note that src is also available in dest to unblock
+       * cycles that src is involved in.
+       */
+
+      for (unsigned i = 0; i < ctx->entry_count; i++) {
+         struct agx_copy *entry = &ctx->entries[i];
+         if (!entry->done && !entry_blocked(entry, ctx)) {
+            entry->done = true;
+            progress = true;
+            do_copy(b, entry);
+            for (unsigned j = 0; j < agx_size_align_16(entry->size); j++) {
+               if (is_real(entry))
+                  ctx->physreg_use_count[entry->src + j]--;
+               ctx->physreg_dest[entry->dest + j] = NULL;
+            }
+         }
+      }
+
+      if (progress)
+         continue;
+
+      /* Step 2: Find partially blocked copies and split them. In the
+       * mergedregs case, we can 32-bit copies which are only blocked on one
+       * 16-bit half, and splitting them helps get things moving.
+       *
+       * We can skip splitting copies if the source isn't a register,
+       * however, because it does not unblock anything and therefore doesn't
+       * contribute to making forward progress with step 1. These copies
+       * should still be resolved eventually in step 1 because they can't be
+       * part of a cycle.
+       */
+      for (unsigned i = 0; i < ctx->entry_count; i++) {
+         struct agx_copy *entry = &ctx->entries[i];
+         if (entry->done || (agx_size_align_16(entry->size) != 2))
+            continue;
+
+         if (((ctx->physreg_use_count[entry->dest] == 0 ||
+               ctx->physreg_use_count[entry->dest + 1] == 0)) &&
+             is_real(entry)) {
+            split_32bit_copy(ctx, entry);
+            progress = true;
+         }
+      }
+   }
+
+   /* Step 3: resolve cycles through swapping.
+    *
+    * At this point, the transfer graph should consist of only cycles.
+    * The reason is that, given any physreg n_1 that's the source of a
+    * remaining entry, it has a destination n_2, which (because every
+    * copy is blocked) is the source of some other copy whose destination
+    * is n_3, and so we can follow the chain until we get a cycle. If we
+    * reached some other node than n_1:
+    *
+    *  n_1 -> n_2 -> ... -> n_i
+    *          ^             |
+    *          |-------------|
+    *
+    *  then n_2 would be the destination of 2 copies, which is illegal
+    *  (checked above in an assert). So n_1 must be part of a cycle:
+    *
+    *  n_1 -> n_2 -> ... -> n_i
+    *  ^                     |
+    *  |---------------------|
+    *
+    *  and this must be only cycle n_1 is involved in, because any other
+    *  path starting from n_1 would also have to end in n_1, resulting in
+    *  a node somewhere along the way being the destination of 2 copies
+    *  when the 2 paths merge.
+    *
+    *  The way we resolve the cycle is through picking a copy (n_1, n_2)
+    *  and swapping n_1 and n_2. This moves n_1 to n_2, so n_2 is taken
+    *  out of the cycle:
+    *
+    *  n_1 -> ... -> n_i
+    *  ^              |
+    *  |--------------|
+    *
+    *  and we can keep repeating this until the cycle is empty.
+    */
+
+   for (unsigned i = 0; i < ctx->entry_count; i++) {
+      struct agx_copy *entry = &ctx->entries[i];
+      if (entry->done)
+         continue;
+
+      assert(is_real(entry));
+
+      /* catch trivial copies */
+      if (entry->dest == entry->src) {
+         entry->done = true;
+         continue;
+      }
+
+      do_swap(b, entry);
+
+      /* Split any blocking copies whose sources are only partially
+       * contained within our destination.
+       */
+      if (agx_size_align_16(entry->size) == 1) {
+         for (unsigned j = 0; j < ctx->entry_count; j++) {
+            struct agx_copy *blocking = &ctx->entries[j];
+
+            if (blocking->done)
+               continue;
+
+            if (blocking->src <= entry->dest &&
+                blocking->src + 1 >= entry->dest &&
+                agx_size_align_16(blocking->size) == 2) {
+               split_32bit_copy(ctx, blocking);
+            }
+         }
+      }
+
+      /* Update sources of blocking copies.
+       *
+       * Note: at this point, every blocking copy's source should be
+       * contained within our destination.
+       */
+      for (unsigned j = 0; j < ctx->entry_count; j++) {
+         struct agx_copy *blocking = &ctx->entries[j];
+         if (blocking->src >= entry->dest &&
+             blocking->src < entry->dest + agx_size_align_16(entry->size)) {
+            blocking->src = entry->src + (blocking->src - entry->dest);
+         }
+      }
+
+      entry->done = true;
+   }
+}
diff --git a/src/asahi/compiler/agx_register_allocate.c b/src/asahi/compiler/agx_register_allocate.c
index 00cba9df194..ffffb1fc71e 100644
--- a/src/asahi/compiler/agx_register_allocate.c
+++ b/src/asahi/compiler/agx_register_allocate.c
@@ -139,6 +139,21 @@ agx_ra_assign_local(agx_block *block, uint8_t *ssa_to_reg, uint8_t *ncomps, unsi
    memcpy(block->regs_out, used_regs, sizeof(used_regs));
 }
 
+/*
+ * Resolve an agx_index of type NORMAL or REGISTER to a physical register, once
+ * registers have been allocated for all SSA values.
+ */
+static unsigned
+agx_index_to_reg(uint8_t *ssa_to_reg, agx_index idx)
+{
+   if (idx.type == AGX_INDEX_NORMAL) {
+      return ssa_to_reg[idx.value];
+   } else {
+      assert(idx.type == AGX_INDEX_REGISTER);
+      return idx.value;
+   }
+}
+
 void
 agx_ra(agx_context *ctx)
 {
@@ -170,57 +185,33 @@ agx_ra(agx_context *ctx)
    agx_foreach_instr_global_safe(ctx, ins) {
       /* Lower away RA pseudo-instructions */
       if (ins->op == AGX_OPCODE_P_COMBINE) {
-         /* TODO: Optimize out the moves! */
-         assert(ins->dest[0].type == AGX_INDEX_NORMAL);
-         enum agx_size common_size = ins->dest[0].size;
-         unsigned base = ssa_to_reg[ins->dest[0].value];
-         unsigned size = common_size == AGX_SIZE_32 ? 2 : 1;
+         unsigned base = agx_index_to_reg(ssa_to_reg, ins->dest[0]);
+         unsigned width = agx_size_align_16(ins->dest[0].size);
+
+         struct agx_copy copies[4];
+         unsigned n = 0;
 
          /* Move the sources */
+         for (unsigned i = 0; i < 4; ++i) {
+            if (agx_is_null(ins->src[i])) continue;
+            assert(ins->src[i].size == ins->dest[0].size);
+
+            copies[n++] = (struct agx_copy) {
+               .dest = base + (i * width),
+               .src = agx_index_to_reg(ssa_to_reg, ins->src[i]) ,
+               .size = ins->src[i].size
+            };
+         }
+
+         /* Lower away the copies pseudo-instruction */
          agx_builder b = agx_init_builder(ctx, agx_after_instr(ins));
-
-         /* TODO: Eliminate the intermediate copy by handling parallel copies */
-         for (unsigned i = 0; i < 4; ++i) {
-            if (agx_is_null(ins->src[i])) continue;
-            unsigned base = ins->src[i].value;
-            if (ins->src[i].type == AGX_INDEX_NORMAL)
-               base = ssa_to_reg[base];
-            else
-               assert(ins->src[i].type == AGX_INDEX_REGISTER);
-
-            assert(ins->src[i].size == common_size);
-
-            agx_mov_to(&b, agx_register(124*2 + (i * size), common_size),
-                  agx_register(base, common_size));
-         }
-
-         for (unsigned i = 0; i < 4; ++i) {
-            if (agx_is_null(ins->src[i])) continue;
-            agx_index src = ins->src[i];
-
-            if (src.type == AGX_INDEX_NORMAL)
-               src = agx_register(alloc[src.value], src.size);
-
-            agx_mov_to(&b, agx_register(base + (i * size), common_size),
-                  agx_register(124*2 + (i * size), common_size));
-         }
-
-         /* We've lowered away, delete the old */
-         agx_remove_instruction(ins);
+         agx_emit_parallel_copies(&b, copies, n);
          continue;
       } else if (ins->op == AGX_OPCODE_P_EXTRACT) {
          /* Uses the destination size */
-         assert(ins->dest[0].type == AGX_INDEX_NORMAL);
-         unsigned base = ins->src[0].value;
-
-         if (ins->src[0].type != AGX_INDEX_REGISTER) {
-            assert(ins->src[0].type == AGX_INDEX_NORMAL);
-            base = alloc[base];
-         }
-
-         unsigned size = ins->dest[0].size == AGX_SIZE_64 ? 4 : ins->dest[0].size == AGX_SIZE_32 ? 2 : 1;
-         unsigned left = ssa_to_reg[ins->dest[0].value];
-         unsigned right = ssa_to_reg[ins->src[0].value] + (size * ins->imm);
+         unsigned size = agx_size_align_16(ins->dest[0].size);
+         unsigned left = agx_index_to_reg(ssa_to_reg, ins->dest[0]);
+         unsigned right = agx_index_to_reg(ssa_to_reg, ins->src[0]) + (size * ins->imm);
 
          if (left != right) {
             agx_builder b = agx_init_builder(ctx, agx_after_instr(ins));
diff --git a/src/asahi/compiler/meson.build b/src/asahi/compiler/meson.build
index 78e87137bfd..b273c10fe16 100644
--- a/src/asahi/compiler/meson.build
+++ b/src/asahi/compiler/meson.build
@@ -23,6 +23,7 @@ libasahi_agx_files = files(
   'agx_compile.c',
   'agx_dce.c',
   'agx_liveness.c',
+  'agx_lower_parallel_copy.c',
   'agx_lower_pseudo.c',
   'agx_pack.c',
   'agx_print.c',