diff --git a/qpms/qpms_c.pyx b/qpms/qpms_c.pyx
index 61cb749..84d0f72 100644
--- a/qpms/qpms_c.pyx
+++ b/qpms/qpms_c.pyx
@@ -1468,12 +1468,15 @@ cdef class ScatteringSystem:
         qpms_scatsys_build_modeproblem_matrix_full(&target_view[0][0], self.s, k)
         return target
 
-    def modeproblem_matrix_packed(self, double k, qpms_iri_t iri):
+    def modeproblem_matrix_packed(self, double k, qpms_iri_t iri, version=None):
         cdef size_t rlen = self.saecv_sizes[iri]
         cdef np.ndarray[np.complex_t, ndim=2] target = np.empty(
                 (rlen,rlen),dtype=complex, order='C')
         cdef cdouble[:,::1] target_view = target
-        qpms_scatsys_build_modeproblem_matrix_irrep_packed(&target_view[0][0], self.s, iri, k)
+        if (version == 'R'):
+            qpms_scatsys_build_modeproblem_matrix_irrep_packed_orbitorderR(&target_view[0][0], self.s, iri, k)
+        else:
+            qpms_scatsys_build_modeproblem_matrix_irrep_packed(&target_view[0][0], self.s, iri, k)
         return target
 
     def translation_matrix_full(self, double k):
diff --git a/qpms/qpms_cdefs.pxd b/qpms/qpms_cdefs.pxd
index 80b60e9..6f21a18 100644
--- a/qpms/qpms_cdefs.pxd
+++ b/qpms/qpms_cdefs.pxd
@@ -291,6 +291,8 @@ cdef extern from "scatsystem.h":
             const qpms_scatsys_t *ss, double k)
     cdouble *qpms_scatsys_build_modeproblem_matrix_irrep_packed(cdouble *target,
             const qpms_scatsys_t *ss, qpms_iri_t iri, double k)
+    cdouble *qpms_scatsys_build_modeproblem_matrix_irrep_packed_orbitorderR(
+            cdouble *target, const qpms_scatsys_t *ss, qpms_iri_t iri, double k)
 
 
 
diff --git a/qpms/scatsystem.c b/qpms/scatsystem.c
index 8e523f6..4878506 100644
--- a/qpms/scatsystem.c
+++ b/qpms/scatsystem.c
@@ -14,6 +14,7 @@
 #include <string.h>
 #include "qpms_error.h"
 #include "translations.h"
+#include <pthread.h>
 
 #define SQ(x) ((x)*(x))
 #define QPMS_SCATSYS_LEN_RTOL 1e-13
@@ -1441,4 +1442,122 @@ complex double *qpms_scatsys_build_modeproblem_matrix_irrep_packed(
   return target_packed;
 }
 
+complex double *qpms_scatsys_build_modeproblem_matrix_irrep_packed_orbitorderR(
+    /// Target memory with capacity for ss->saecv_sizes[iri]**2 elements. If NULL, new will be allocated.
+    complex double *target_packed,
+    const qpms_scatsys_t *ss, qpms_iri_t iri,
+    double k ///< Wave number to use in the translation matrix.
+    )
+{
+  const size_t packedlen = ss->saecv_sizes[iri];
+  if (!packedlen) // THIS IS A BIT PROBLEMATIC, TODO how to deal with empty irreps?
+    return target_packed; 
+  if (target_packed == NULL)
+    target_packed = malloc(SQ(packedlen)*sizeof(complex double));
+  if (target_packed == NULL) abort();
+  memset(target_packed, 0, SQ(packedlen)*sizeof(complex double));
 
+  // some of the following workspaces are probably redundant; TODO optimize later.
+
+  // workspaces for the uncompressed particle<-particle tranlation matrix block
+  // and the result of multiplying with a T-matrix
+  complex double *Sblock, *TSblock;
+  QPMS_CRASHING_MALLOC(Sblock, sizeof(complex double)*SQ(ss->max_bspecn));
+  QPMS_CRASHING_MALLOC(TSblock, sizeof(complex double)*SQ(ss->max_bspecn));
+
+  // Workspace for the intermediate particle-orbit matrix result
+  complex double *tmp;
+  QPMS_CRASHING_MALLOC(tmp, sizeof(complex double) * SQ(ss->max_bspecn) * ss->sym->order);
+
+  const complex double one = 1, zero = 0;
+
+  for(qpms_ss_pi_t opistartR = 0; opistartR < ss->p_count; 
+      opistartR += ss->orbit_types[ss->p_orbitinfo[opistartR].t].size //orbit_p_countR; might write a while() instead
+     ) {
+    const qpms_ss_pi_t orbitstartpiR = ss->p_by_orbit[opistartR];
+    const qpms_ss_oti_t otiR = ss->p_orbitinfo[orbitstartpiR].t;
+    const qpms_ss_osn_t osnR = ss->p_orbitinfo[orbitstartpiR].osn;
+    const qpms_ss_orbit_type_t *const otR = ss->orbit_types + otiR;
+    const qpms_ss_orbit_pi_t orbit_p_countR = otR->size;
+    const size_t orbit_packedsizeR = otR->irbase_sizes[iri];
+
+    if(orbit_packedsizeR) { // avoid zgemm crash on empty irrep
+      const size_t particle_fullsizeR = otR->bspecn; // == bspecR->n
+      const qpms_vswf_set_spec_t *bspecR = ss->tm[ss->p[orbitstartpiR].tmatrix_id]->spec;
+      // This is the orbit-level matrix projecting the whole orbit onto the irrep.
+      const complex double *omR = otR->irbases + otR->irbase_offsets[iri];
+      // Orbit coeff vector's full size:
+      const size_t orbit_fullsizeR = otR->size * otR->bspecn;
+      // This is where the orbit starts in the "packed" vector:
+      const size_t packed_orbit_offsetR =
+        ss->saecv_ot_offsets[iri*ss->orbit_type_count + otiR] 
+        + osnR * otR->irbase_sizes[iri];
+      for(qpms_ss_orbit_pi_t opiR = 0; opiR < orbit_p_countR; ++opiR) {
+        qpms_ss_pi_t piR = ss->p_by_orbit[opistartR + opiR];
+        assert(opiR == ss->p_orbitinfo[piR].p);
+        const qpms_ss_oti_t otiR = ss->p_orbitinfo[piR].t;
+        assert(ss->p_orbitinfo[piR].osn == osnR);
+        const cart3_t posR = ss->p[piR].pos;
+        // dest particle T-matrix
+        const complex double *tmmR = ss->tm[ss->p[piR].tmatrix_id]->m;
+        for(qpms_ss_pi_t piC = 0; piC < ss->p_count; ++piC) { //Column loop
+          const qpms_ss_oti_t otiC = ss->p_orbitinfo[piC].t;
+          const qpms_ss_orbit_type_t *const otC = ss->orbit_types + otiC;
+          const qpms_ss_osn_t osnC = ss->p_orbitinfo[piC].osn;
+          const qpms_ss_orbit_pi_t opiC = ss->p_orbitinfo[piC].p;
+          // This is where the particle's orbit starts in the "packed" vector:
+          const size_t packed_orbit_offsetC = 
+            ss->saecv_ot_offsets[iri*ss->orbit_type_count + otiC]
+            + osnC * otC->irbase_sizes[iri];
+          const qpms_vswf_set_spec_t *bspecC = ss->tm[ss->p[piC].tmatrix_id]->spec;
+          // Orbit coeff vector's full size:
+          const size_t orbit_fullsizeC = otC->size * otC->bspecn;
+          const size_t particle_fullsizeC = otC->bspecn; // == bspecC->n
+          const size_t orbit_packedsizeC = otC->irbase_sizes[iri];
+          // This is the orbit-level matrix projecting the whole orbit onto the irrep.
+          const complex double *omC = otC->irbases + otC->irbase_offsets[iri];
+
+          if(orbit_packedsizeC) { // avoid zgemm crash on empty irrep
+            if(piC != piR) { // non-diagonal, calculate TS
+              const cart3_t posC = ss->p[piC].pos;
+              QPMS_ENSURE_SUCCESS(qpms_trans_calculator_get_trans_array_lc3p(ss->c,
+                    Sblock, // Sblock is S(piR->piC)
+                    bspecR, bspecC->n, bspecC, 1,
+                    k, posR, posC));
+
+              cblas_zgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans,
+                  bspecR->n /*m*/, bspecC->n /*n*/, bspecR->n /*k*/,
+                  &one/*alpha*/, tmmR/*a*/, bspecR->n/*lda*/,
+                  Sblock/*b*/, bspecC->n/*ldb*/, &zero/*beta*/,
+                  TSblock /*c*/, bspecC->n /*ldc*/);
+            } else { // diagonal, fill with diagonal -1
+              for (size_t row = 0; row < bspecR->n; ++row)
+                for (size_t col = 0; col < bspecC->n; ++col)
+                  TSblock[row * bspecC->n + col] = (row == col)? -1 : 0;
+            }
+
+            // tmp[oiR|piR,piC] = ∑_K M[piR,K] U*[K,piC]
+            cblas_zgemm(CblasRowMajor, CblasNoTrans, CblasConjTrans,
+                particle_fullsizeR /*M*/, orbit_packedsizeC /*N*/, particle_fullsizeC /*K*/,
+                &one /*alpha*/, TSblock/*A*/, particle_fullsizeC/*ldA*/, 
+                omC + opiC*particle_fullsizeC /*B*/,
+                orbit_fullsizeC/*ldB*/, &zero /*beta*/,
+                tmp /*C*/, orbit_packedsizeC /*LDC*/);
+
+            // target[oiR|piR,oiC|piC] += U[...] tmp[...]
+            cblas_zgemm(CblasRowMajor, CblasNoTrans, CblasNoTrans,
+                orbit_packedsizeR /*M*/, orbit_packedsizeC /*N*/, particle_fullsizeR /*K*/,
+                &one /*alpha*/, omR + opiR*particle_fullsizeR/*A*/, orbit_fullsizeR/*ldA*/,
+                tmp /*B*/, orbit_packedsizeC /*ldB*/, &one /*beta*/,
+                target_packed + packedlen*packed_orbit_offsetR + packed_orbit_offsetC /*C*/,
+                packedlen /*ldC*/);
+          }
+        }
+      }
+    }
+  }
+  free(tmp);
+  free(Sblock);
+  free(TSblock);
+  return target_packed;
+}
diff --git a/qpms/scatsystem.h b/qpms/scatsystem.h
index 5616767..bf42990 100644
--- a/qpms/scatsystem.h
+++ b/qpms/scatsystem.h
@@ -486,12 +486,20 @@ complex double *qpms_scatsys_build_modeproblem_matrix_full(
 		const qpms_scatsys_t *ss,
 		double k ///< Wave number to use in the translation matrix.
 		);
+/// Creates the mode problem matrix directly in the irrep-packed form.
 complex double *qpms_scatsys_build_modeproblem_matrix_irrep_packed(
 		/// Target memory with capacity for ss->fecv_size**2 elements. If NULL, new will be allocated.
 		complex double *target,
 		const qpms_scatsys_t *ss, qpms_iri_t iri,
 		double k ///< Wave number to use in the translation matrix.
 		);
+/// Alternative implementation of qpms_scatsys_build_modeproblem_matrix_irrep_packed().
+complex double *qpms_scatsys_build_modeproblem_matrix_irrep_packed_orbitorderR(
+		/// Target memory with capacity for ss->fecv_size**2 elements. If NULL, new will be allocated.
+		complex double *target,
+		const qpms_scatsys_t *ss, qpms_iri_t iri,
+		double k ///< Wave number to use in the translation matrix.
+		);
 
 /// NOT IMPLEMENTED Dumps a qpms_scatsys_t structure to a file.
 qpms_errno_t qpms_scatsys_dump(qpms_scatsys_t *ss, char *path);